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Hate crime is a crime where the motive is the victim's affiliation (or perceived affiliation) to a particular social group, like race, religion, sexual orientation, disability, ethnicity, nationality, age, gender, gender identity, or political affiliation. These crimes produce the intimidation of other individuals pertaining to the victim's group.
The best understanding (and the more legally specific term that should have been used when writing these laws) is "domestic terrorism" or "bias-motivated crime". By application and description, a hate crime is not a crime that simply involves the hatred of one person over another, but is in fact an attack on an entire group by a single act of violence. It implicitly aims to send a message of fear to those individuals who are part of the stigmatized group, warning that they should "watch themselves", not "cross the line", or "get uppity".
The term is not 100% literal, and "hate crime" specifically does not refer to any crimes that involve any degree of hate. That is dumb and quite pointless — almost every crime would then be a "hate crime," and we'd instead be looking for a term to describe non-hate crimes.
Notable hate crimes in the US not tried as hate crimes, 'cause the victims were not part of the right 'group'
- Vincent Chin, 1982. Chinese American, beaten to death with a baseball bat by two guys who blamed the Japanese for "stealing all their jobs".
- Brandon Teena, 1993. Transgender.
- James Byrd Jr., 1998 Dragged by a truck for two miles, until his death by decapitation. Terrifyingly, he is believed to have been conscious for most of the ordeal. Texas, a good ol' southern state, did not have any laws providing sentence enhancement for bias-motivated crimes. His murder was the impetus for Texas to pass its first Hate Crime law in 2001; two of the perpetrators were sentenced to death and the third to life in prison. Though his name is often left out, he is listed on the (officially titled) Matthew Shepard and James Byrd, Jr. Hate Crimes Prevention Act, 2009.
- Matthew Shepard, also murdered in 1998. It gave rise to the 2009 (Federal) Matthew Shepard Hate Crime Prevention Act.
- Roberto González Onrubia, 2007, Spain. Spain does not recognize hate crimes done to women, gays, or transgender persons.
National hate crime laws
Most modern "Western" countries have some hate crimes on the books for race, religion, and national origin. Some include age and gender, and a few include sexual orientation and gender identity.
- Australia — The Racial Discrimination Act covers acts done due to "race, colour or national or ethnic origin" of another person, or of some or all of the people in a group.
- Canada — offence was motivated by bias, prejudice or hate based on race, national or ethnic origin, language, colour, religion, sex, age, mental or physical disability, sexual orientation, or any other similar factor. Canada's laws affect the sentencing. Canada's laws are intentionally open ended to allow for groups which are not listed, to appeal to the judge for consideration of "bias motivation," including (not necessarily successfully) political groups or activist groups.
- European Union — specifically addresses hate crimes done over the internet.
- France — applies harsher sentence for crimes against actual or perceived ethnicity, nation, race, religion, or sexual orientation.
- Finland — applies to race, ethnicity, or national origin; does not (per wikipedia) protect gender, age or sexual orientation. Has specific language to protect protesters of any political, religious or social group from "backlash".
- Germany — criminalizes hate speech and applies only to the judicial sentencing after the trial.
- Ireland — specifies: race, color, nationality, religion, sexual orientation, ethnic or national origins, or membership of the Traveller community, an indigenous minority group.
- Italy — allows enhanced sentencing for crimes motivated by race, ethnicity, or religion but not gender, gender identity or sexual orientation.
- Norway — longer sentences for violent crime where motivated by skin color, ethnic or national origin, religion, orientation, or disability 
- United Kingdom overall — general provisions specifies racial groups and religious groups only. There are no general provisions for sexual orientation, age, or gender. However, laws vary across the UK in smaller government units. Scotland, for example, allows the lawyer and judge to apply the law to anyone who makes a claim that he or she belongs to a targeted "group" of any type. The judge has discretion to decide if that group qualifies for protection (from age and gender, to particular social or sports groups have tried to use this provision).
- US Federal — Hate Crime laws originally protected race, religion, and national origin. In 2009, the Matthew Shepard bill added gender, gender identity, and sexual orientation. These are applicable only to federal crimes.
- US States — 45 US States have some kind of hate crime laws on the books, but they vary in coverage and how they can be applied (ie are they a crime in and of themselves, or only a part of the sentencing system).
- "Uppity" is a term most often associated with the women's movement in the US, during the late 1950s through the early 1970s. But in the "good old days", the adjective "uppity" saw use generally in reference to members of the group then known as "niggers": see https://books.google.com/ngrams/graph?content=uppity%2C+uppity+nigger%2C+uppity+woman&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cuppity%3B%2Cc0%3B.t1%3B%2Cuppity%20nigger%3B%2Cc0%3B.t1%3B%2Cuppity%20woman%3B%2Cc0
- Straffeloven (Criminal Code) Part 2 Chapter 25 §272 Paragraph E