Nihilistic anarchist who may have coined the phrase "the will to destroy is a creative urge". During a brief association with Bakunin, a number of pamphlets appeared which may have been written by either or both of them, most famously "Catechism of a Revolution". The two soon fell out because Bakunin was not really a nihilist.
Nechaev's ideal was for revolutionaries to be utterly ruthless and prepared to take any action, however apparently immoral, which would further their cause (a bit like politicians, in other words).
Exiled from Russia after being accused of murdering a political associate; eventually deported to Russia and killed by the state.
To "do a Nechaev" is to act nihilistically. Most often used along the lines of, "I wasn't feeling like doing a Nechaev" (i.e. not feeling like extreme self-sacrifice and escalation).