A duo consisting of singer Alan Vega and keyboard player Martin Rev. Suicide first gained notice in the mid-1970s, playing in New York's glam / cross-dresser scene, with Vega's dark and half-sung, half-screamed vocals. Rev started out playing a Farfisa combo organ, run through a variety of distortion devices, but began adding second-hand synthesizers. Vega labeled their music as "punk" and is sometimes said to have been the person to attach that name to that style of music, despite the fact that Suicide did not have a guitar player.

Playing in punk clubs, making strange noises with often-malfunctioning synths and cheap drum machines earned Suicide much enmity from a sector of the audience, at clubs such as CBGB's where the audience had come to see more conventional (so to speak) punk bands. Booing and insults from the audience was common -- and Vega and Rev returned the favor from the stage, with the result that many of their early shows ended in brawls. However, connoisseurs of New York's art scene regarded Suicide as revolutionary, and the duo proved capable of producing engaging songs despite minimal instrumentation.

Suicide released their first, eponymous album in 1977. Ric Ocasek, singer/guitarist of the New Wave band The Cars, took an interest in them and began billing them as an opening act for The Cars' tours, despite the vast differences in their musical styles. Ocasek produced their second album, which was also titled Suicide, but the record company insisted on re-titling it Suicide: Alan Vega and Martin Rev to avoid confusion. The duo also released several live albums during this period, including one recording of a notorious concert in Brussels which ended in a riot.

After 1985, Vega and Rev began to record solo albums and collaborations with other artists. Although they continued to perform together and released a number of live recordings, Suicide would release only three more albums of all-new studio material, the last in 2002. Rev became interested in electronica and did a number of performances as both a producer and DJ. He is still performing; Vega died in 2016.