Ayatollah Ali Khamenei is the Supreme Leader of Iran, serving since June 4th, 1989, the day after Ruhollah Khomeini's death. He was once the President of Iran in the 1980s, before the clergy picked him to succeed Khomeini. The nature of his job highlights the "Islamic" part of the "Islamic Republic of Iran" and plays down the "republic" part: he can overrule any acts of the Iranian legislature and president. He lacks Khomeini's charisma or clerical standing, and compensates by being something of a recluse, remaining aloof from day-to-day politics, giving no press conferences or interviews and leaving the President as the face of Iran.
Despite all the bluster of Iran getting nukes (or having nukes; nobody seems to make up their minds anymore), Khamenei has issued a fatwa (basically a religious executive command) saying the production, stockpiling and use of nuclear weapons was forbidden under Islam in Iran. The Islamic Republic has since signed the Nuclear Non-Proliferation Treaty, something only Israel, India and Pakistan have not done in the region.
He's not a fan of criticism directed at him, however. According to law, "spreading libel against officials, institutions, organizations and individuals in the country or insulting legal or real persons who are lawfully respected, even by means of pictures or caricatures" is not allowed. Therefore, opposition journalists Ahmad Zeidabadi, Mohsen Sazegara, Mohammad Nourizad and Akbar Ganji were arrested and investigated for spreading critical articles containing unproven charges against Khamenei's policies as the leader and some organizations. He once rejected a 2000 bill presented by the Iranian parliament that aimed to reform the country's press law, and the Guardian Council (which approves of parliamentary candidates) disqualified thousands of 2004 electoral parliamentary candidates who wanted freedom of the press.
Just so you know he fully lives up to the "Supreme Leader" title, we will count the ways. He has a shitstorm of commissars stationed in strategic posts throughout government bureaucracies, dedicated to inspecting and observing the administrations; it's how he knew who to disqualify of all those candidates mentioned above. The leaders of the Islamic Revolutionary Guards, a hardline agency of Muslim Iranians, are directly appointed by, and publicly deferential to Khamenei. They have been rising rapidly and alarmingly, essentially being a slightly less scrutinized and more powerful version of the Tea Party in America. It's gotten to a point where the Revolutionary Guards are the second anchor in the Iranian regime, just after the Supreme Leader. The weak, conservative-dominated parliament is headed by Khamenei loyalist Gholam-Ali Haddad-Adel, whose daughter is married to Khamenei's son. Most glaringly, in the 2005 presidential election, hardliner Mahmoud Ahmadinejad trounced Khamenei's chief rival, Hashemi Rafsanjani, and he doubtlessly played a part in Ahmadinejad's bogus landslide re-election (as well as the crackdown on protesters). Nevertheless, he's had to slap Ahmadinejad every so often when the latter proved too damn dumb for his tastes.
Following the election of Hassan Rouhani, Khamenei's been uncharacteristically tolerant of the attempts at diplomacy Rouhani's been spearheading with the West. He has indicated he didn't like Rouhani's direct phone call with Barack Obama, but he's stayed away from doing anything else. In fact, he actually endorsed Rouhani for the presidency, preferring the moderate to the hardliners surrounding him. Which is rather smart of Khamenei, by the way, since Iran is suffering from economic sanctions directed by the West; he needs whatever silver lining he can get so Iran is free of economic turmoil, and Rouhani is that silver lining. He's said he trusts Rouhani enough to give the latter full authority to negotiate on Iran's nuclear program with America. We are not looking forward to the future if the diplomacy doesn't work out.