Impeachment refers to the initiation of a legal process where the legislative branch removes a member of the legislative, judiciary or executive branch for committing high crimes and misdemeanors. It is commonly available in presidential systems to remove a criminal president who would otherwise serve out their term, but in parliamentary systems, a simple vote in parliament is usually enough to be rid of naughty heads of government or officials without the trouble of having to vote for impeachment then go through the rigmarole of impeaching. Impeachments of both politicians and judges tend to be rare, because the accused usually sees the way things are going and quits before formal impeachment.
Impeachment is often viewed as a necessary power because it is unclear under US law if a president can be prosecuted in any court other than an impeachment proceeding for criminal offences, and the president can't be dismissed unless incapable (which is different from immoral or illegal). In other countries such as France, the President is formally immune from all criminal charges unless impeached or if they otherwise leave office (e.g. after losing an election). So impeachment is a way of prosecuting the otherwise unprosecutable.
The British Parliament saw impeachment as the only way to have any measure of control over the King or ministers who were favorites of the King. The first example of impeachment appears in 1386 charging Michael de la Pole, Earl of Suffolk. Though some of the charges included common law offenses (purchasing land from the King at a lower price than its worth), other charges included promises he had broken to Parliament and failing to use funds appropriated by Parliament to pay a ransom. The House of Commons would vote on impeachment over 100 times between 1620 and 1649. In the midst of the British Civil war, the House of Commons sought to remove Thomas Wentworth, Earl of Strafford. The first article of impeachment included:
That he… hath traiterously endeavored to subvert the Fundamental Laws of the Government of the Realms… and in stead therof, to introduce Arbitrary and Tyrannical Government against Law…
Fundamentally the House of Commons saw that crimes against the system of government as impeachable. Charges often included; treason, high treason, misdemeanors, malversations and high crimes and misdemeanors. After the execution of Charles I, impeachment was absent in legal records until 1660, when Charles II was restored, and Parliament expanded the definition of "high Crimes and Misdemeanors" to include negligent discharge of duties and improprieties in office. The impeachment of Warren Hastings is also important in the history of impeachment. Hastings was the first Governor-General of India. Among the high crimes and misdemeanors, Hastings was charged with was gross maladministration, corruption in office and cruelty toward the people of India. The impeachment process, which began in 1786 and ended in 1795, was observed closely by members of the United States Constitutional Convention.
Constitutional Convention debate
The Constitutional Convention vigorously debated including impeachment in the burgeoning Constitution. Initially there were concerns that such a remedy would make the executive "the Minion of the Senate". Among the discussions in limiting the power of the executive, there was a discussion to make it a position held by multiple individuals. This was rejected, primarily by Alexander Hamilton in Federalist No. 70, as it would deprive the people of the ability to censure and punish those entrusted to faithfully exercise power. Additionally the level of responsibility is diminished with each party of an empowered executive. Philadelphia delegate William R. Davie would provide another example, that the public would have a clearer notion of who was to blame. Initially the power of impeachment was to be limited to treason and bribery. George Mason found these grounds too limited:
Why is the provision restrained to Treason & bribery only? Treason as defined in the Constitution will not reach many great and dangerous offenses. Hastings is not guilty of Treason. Attempts to subvert the Constitution may not be Treason as above defined — As bills of attainder which have saved the British Constitution are forbidden, it is the more necessary to extend: the power of impeachments.
Mason suggested adding the phrase maladministration, but when Madison objected to the vagueness of the term, Mason instead submitted "high crimes and misdemeanors against the State" which was adopted by the convention without further debate.
High crimes and misdemeanors
Federalist 65, taken with the notes from the Convention, and knowledge of the delegates' legal indication, made it clear that the adopted language was to mirror that of British legal interpretation. It also had previously deployed this phrase in reference to extradition from one state to another. It also included crimes to avoid any comparison to the parliamentary term "high misdemeanor", defined in Commentaries on the Laws of England, which included positive offenses against the king and government, though the principal high misdemeanor was "mal-administration of such high officers, as are in the public trust and employment". The Supreme Court has held that the phrase is a term of art, meant only to be interpreted by the Framers' intention. From Chief Justice John Marshall:
It is a technical term. It is used in a very old statute of that country whose language is our language, and whose laws form the substratum of our laws. It is scarcely conceivable that the term was not employed by the framers of our constitution in the sense which had been affixed to it by those from whom we borrowed it.
Impeachment before Nixon
In 1974, the 93rd Congress was examining grounds for impeachment against Richard M. Nixon for his actions regarding Watergate. The Committee on the Judiciary of he House of Representatives authorized a report titled Constitutional Grounds for Presidential Impeachment.  The document isn't particularly long (64 pages, but only 26 pages of analysis), breaks down the history of impeachment (of which the previous two sections are borrowed), including the history of impeachment in the United States. From 1787 to the time of the report, the House impeached thirteen officers including one President, Andrew Johnson, one Cabinet Officer, Secretary of War William W. Belknap, one US Senator, William Blount of Tennessee, and ten federal judges. In all of these cases, the impeachable conduct falls into three broad categories:
- Exceeding the constitutional bounds of the office in derogation of the powers of another branch of government
- Behaving in a manner grossly incompatible with the proper function and purpose of the office
- Employing the power of the office for an improper purpose or for personal gain
Exceeding the constitutional bounds of the office in derogation of the powers of another branch of government
These were the grounds for which they impeached Senator Blount. The allegation was that Blount attempted to incite two Indian tribes to attack Spanish settlers in Florida and Louisiana, eventually planning to seize the territory for the British. These were also the grounds used to impeach President Johnson after he had removed the Senate-confirmed Secretary of War, Edwin Stanton, and replaced him with someone more aligned with himself on matters of Reconstruction. Neither of these impeachment cases resulted in conviction by the Senate.
Behaving in a manner grossly incompatible with the proper function and purpose of the office
These were the grounds of impeachment for several judges, including intoxication on the bench and partisan views influencing conduct. Another was for joining the Confederacy and not resigning, as well as examples of favoritism.
Employing the power of the office for an improper purpose or for personal gain
Primarily these are instances where federal judges have used their authority vindictively or used their office for personal gain. These include instances of federal judges threatening and imprisoning journalists and lawyers. This served as the grounds for impeaching Secretary Belknap, who was accused of improperly appointing a post trader at a frontier military post in Indian Territory and receiving payments through an intermediary.
In the United States, the POTUS and other officials may be removed from office by Congress after being impeached and convicted. The process, outlined in the Constitution, begins when the full House of Representatives assigns a committee of jurisdiction, usually Judiciary Committee to draw up articles of impeachment against the official to be impeached. After much debate, the full House then votes on them. Article II Section 4 assigns the sole power of impeachments to the House. A single member such as the Speaker, or group of members such as a committee, cannot gain judicial enforcement of its subpoena power to potentially override claims of Executive Privilege if a crime has been alleged without authorization from the full House.
If any of the articles so drawn up receives a majority of votes in favor, this is presented as a formal accusation, or indictment, before the US Senate. (The official at this point has been impeached, but not convicted.) In the Senate, the matter is tried in a manner similar to a criminal case. The chief justice of the United States sits as the presiding officer under the Rules of the Senate when the case is against the president or vice president; otherwise the vice president presides. The Senate sits as a High Court of Impeachment in which senators consider evidence, hear witnesses, and vote to acquit or convict the impeached official.
A common misconception is that impeachment trials are similar to common judicial trials as far as rules and standards go. However, this is not the case: the Senate holds a vote before the impeachment trial on what rules to adopt for the proceedings. For example, Hearsay is typically inadmissible in judicial trials (with about a bazillion exceptions), but the Senate does not have to adopt that standard of evidence or testimony. This can have various effects on the trial's procedures. During Donald Trump's first impeachment trial, the Republican Senate voted not to allow witnesses, which greatly damaged the House's ability to make their arguments, as much of their case relied on firsthand witness testimony. During Trump's second impeachment trial, both parties agreed that most of the factual arguments did not need witness corroboration so they decided not to allow witnesses for serendipity (although the trial ended up lasting four days anyway).
After both sides have finished presenting their cases, the Senate votes on whether or not to remove the official in question. It takes a two-thirds majority to remove the person; the proceedings usually also involve a ban on ever holding public office again. The Senate takes a separate vote over whether to ban said individual from serving in the government again; this requires a simple majority. Though this action tends to have a greater effect on removals from the Judicial or Legislative branch, there has been little attention paid to it used against the Executive, as there hadn't been Senate impeachment proceedings in the Executive branch since (as of 2019) the impeachments of Andrew Johnson (in 1868) and Bill Clinton (in 1999). In addition to impeachment, the official may also be tried in a separate action for criminal conduct in court. In 1797 the House impeached Senator Blount but the Senate decided Senators could not be impeached and instead expelled him.
Since 1974 there have been six impeachment proceedings, including five of federal judges, ranging from bribery, to perjury, to tax evasion and sexual assault. President Bill Clinton was the subject of an impeachment recommendation in connection with lies under oath to a federal judge in a sexual harassment case regarding questions of an extra-marital affair with then White House staffer Monica Lewinsky. An added irony, is the 1974 document was co-written by then lawyer, but future First Lady Hillary Clinton. Clinton survived the impeachment, as the Senate failed to convict the President.
Trump and impeachment
Following the report from Bob Mueller about Russian interference in the 2016 Presidential election, impeachment has been top of mind for many Congressional Democrats and various grassroots campaigns. The report details ten examples that could meet the legal definition of obstruction of justice. Failing that high legal standard, there is definitely an argument that all of these events would meet the standard of exceeding the constitutional bounds of the President (witness tampering, promising pardons) and behaving in a manner grossly incompatible with the office of the President (Look at his Twitter account). House investigators as well as the media have also been examining whether Trump is using the office of the President for his own personal gain, but those investigations are ongoing.
Trump actually managed to get an impeachment inquiry opened against him, after a call between himself and the President of Ukraine revealed that he pressured the Ukrainian government to assist in recovering DNC servers from CrowdStrike, investigating a baseless conspiracy theory, and gathering political dirt on a 2020 political opponent (Joe Biden). Nancy Pelosi (D-CA) announced the inquiry on September 24, 2019, which would be led by the heads of six committees. Following the release of a whistleblower complaint, the House Permanent Select Committee on Intelligence, led by Adam Schiff (D-CA), has taken the leading role subpoenaing documents and testimony from multiple people involved with this scandal, including Trump's personal attorney
and soon to be prison inmate Rudy Giuliani.
Trump has reacted poorly to the inquiry, intimating that the whistleblower is a spy and should be executed as well as attacking Committee Chair Schiff as a "traitor" and implying that his being removed from the Presidency would result in a civil war. Though Trump has a history of unhinged and inflammatory tweets, there seems to be a new level of insanity and dangerous rhetoric coming from the Tweeter-in-Chief. As of September 30, 2019, there were 224 members of Congress who support an impeachment inquiry, including all House Democrats, one independent, and one Republican. On October 3, while being interviewed on the White House lawn, Trump again suggested that the Ukrainian government should open an investigation into the Bidens, while adding that he felt that China should do the same.
On October 8, 2019, the White House responded to the alleged "impeachment inquiry".
Counsels for President Trump argued that since the full House failed to authorize a committee of jurisdiction with subpoena power, Article II of the impeachment resolution, alleging Obstruction of Congress, would breakdown the separation of powers and turn the American system into a parliamentary system where impeachment becomes a routine "vote of no confidence"; the Article I charge of Abuse of Power was alleged to be too vague and lacked a specific crime. Trump defense attorney's argued the impeachment articles were built on a "corrupt motive theory" and would set a dangerous precedent, criminalizing policy disputes.
In the wake of Trump's overt incitement of violent activity that led to the 2021 U.S. Capitol riot, there were calls from various parties, including historians to impeach him for a second time. At the time of the calls for impeachment, there was under 2 weeks left before Joe Biden would be inaugurated, and thus the impact would seem to be primarily symbolic. However, if the impeachment and conviction is successful, it could stop Trump from running for political office in future, most importantly re-running for president in 2024. 
Trump was impeached for a second time on January 13, 2021, with the House vote being 232-197. All 222 Democrats and 10 Republicans voted in favor of impeachment. This was the first time in American history that a president was impeached twice. The House formally transferred the single article of impeachment late January 25, 2021. Senators were sworn in as members of the jury the next day. Unlike previous impeachments the Chief Justice will not preside, because it does not involve a sitting Executive, instead Senate Pro Tempore Patrick Leahy (D-VT) will preside. Following an agreement between Democratic leader Schumer and Republican leader McConnell, the trial will began on February 8th, 2021.
A Bad Argument
Senate Republicans have shown their true intentions in a new defense they trotted out against impeachment. The logic being that because Trump is no longer in office, he cannot be impeached. Besides the lunacy of continuing to support someone that riled up their supporters to kill you, and that Trump's Twitter fingers are silent, it also is historically inaccurate. Sen. William Blount, mentioned above, tried to use this exact argument in 1798. The Senate expelled him before the impeachment trial, but the argument that because he was no longer a Senator was the not reasoning for his acquittal. Secretary of War William Belknap, also mentioned above, attempted this argument as well, resigning before the House could impeach him. The House still impeached him in 1876. Two modern impeachments involving judges, the Senate declined to proceed with a trial after resignations, however expressly reserved the power to impeach after resignation. Though the motion is expressly not rooted in Constitutional logic or precedent, it is an early indicator that reaching two thirds for conviction is unlikely.
Initial statements were submitted by the House Impeachment managers  and Trump's defense team. A week before the trial is set to begin, each statement both reiterated arguments from the Jan 25 Senate vote and projected likely arguments to be made during the trial. The House Impeachment managers lay the blame for insurrection at the feet of Trump, and intend to detail how the weeks long effort to overturn the results of the 2020 election violated his oath of office. Trump's defense team, replacing his previous defense team, doubled down on the baseless claims of voter fraud with it's opening salvo, including this howler:
Trump’s lawyers, Bruce Castor and David Schoen, also advanced the former president’s false claims that the election results were “suspect,” asserting that Trump has a First Amendment right to express that view.
“Insufficient evidence exists upon which a reasonable jurist could conclude that the 45th president’s statements were accurate or not, and he therefore denies they were false,” Castor and Schoen wrote, adding that Trump “denies” it is false to say he won the election “in a landslide.”
Castor and Schoen both have dubious histories in litigation. Castor made a secret deal in 2005 with Bill Cosby to not pursue charges against the comedian while district attorney for Montgomery County, Pennsylvania and Schoen previously worked with Roger Stone, also planned to work with Jeffery Epstein, before his death, who Schoen believes was murdered.
In other countries
Impeachment is strongly associated with the US and other presidential systems; it is less common in parliamentary democracies where the head of government can be removed by a parliamentary vote. In France the President can be impeached by a parliamentary court (per article 68 of the constitution of the Fifth Republic); in India the President can be impeached but never has; while in Germany the President (who has a largely ceremonial role) can be impeached but the head of government, the Chancellor, must be kicked out by the Bundestag. In Russia, there were attempts to impeach Boris Yeltsin in the late 1990s, but they never got the votes in the Duma, the lower house of parliament, to proceed. In 2008, then-President Pervez Musharraf of Pakistan was threatened with impeachment for twice seizing power illegally, but quit rather than face charges.
In the UK, it is theoretically available for members of the House of Lords and commoners "beyond the reach of the law or which no other authority in the state will prosecute", typically used against government ministers. However legal authorities consider it probably obsolete and in 1967 the Select Committee on Parliamentary Privilege recommended its abolition, on the basis that ministers can be prosecuted in court or dismissed by parliament. The last impeachment was in 1806, of the Tory minister Henry Dundas, who was acquitted of misappropriating Admiralty funds. There was an unsuccessful attempt to impeach Tony Blair in 2004 over the Iraq War, and calls by members of parliament for Boris Johnson's impeachment over his unlawful prorogation of parliament in September 2019, but neither came to much.
- LII Backgrounder on Impeachment, Cornell University Law School
- Representative Barbara Jordan's "Inquisitor speech"
- See the Wikipedia article on Impeachment investigations of United States federal judges.
- Can a sitting U.S. president face criminal charges?, Reuters, Feb 26, 2019
- See the Wikipedia article on President of France.
- J. Rushworth, The Tryal of Thomas Earl of Stafford, in 8 Historical Collections 8 (1686)
- Blackstone's Commentaries 121
- US v. Burr, 25 Fed. Cas. 1, 159 (No. 14, 693) (C.C.D. Va. 1807)
- United States Senate. Impeachment. https://www.cop.senate.gov/ - "The Senate sits as a High Court of Impeachment in which senators consider evidence, hear witnesses, and vote to acquit or convict the impeached official."
- Ukraine transcript reveals Trump asked for 'favor' related to CrowdStrike conspiracy theory, by Jerry Dunleavy, Washington Examiner, September 26, 2019.
- Complete List: Who Supports an Impeachment Inquiry Against Trump? by Alicia Parlapiano et al. (Updated Sept. 30, 2019 at 12:15 P.M. ET) The New York Times.
- Mark Amodei Becomes First House Republican to Publicly Support Impeachment Inquiry by Daniel Politi (Sept 28, 20196:01 PM) Slate.
- Trump says China should investigate the Bidens amid impeachment furor by Caitlin Oprysko (Updated Oct. 3, 2019 at 5:18 P.M. ET) Politico.
- Letter from Pat Cipollone, Counsel to the President to Speaker Pelosi and Chairmen Engels, Schiff, and Cummings, October 8, 2019.
- Hundreds of historians call for Trump's removal from office (January 11, 2021) 'AP via MSNBC.
- Trump impeachment: Democrats formally charge president with inciting insurrection by Tom McCarthy (11 Jan 2021 14.06 EST) The Guardian.
-  (January 25, 2021) Politico.
- See the Wikipedia article on Impeachment.
- See the Wikipedia article on Pervez Musharraf.
- Glossary: Impeachment, UK Parliament Website
- See the Wikipedia article on Henry Dundas, 1st Viscount Melville.
- See the Wikipedia article on Impeachment in the United Kingdom.
- See the Wikipedia article on Parliamentary motion to impeach Tony Blair.
- Could Boris Johnson be impeached?, Metro, 26 Sep 2019