Their lineup rotated frequently during their existence, with the husband-and-wife duo of singer Lux Interior and guitarist Poison Ivy the only ever-present members.

In the late 1970s, the Cramps briefly shared a rehearsal space with the Fleshtones, and performed regularly in New York at clubs such as CBGB and Max's Kansas City, releasing two independent singles produced by Alex Chilton at Ardent Studios in Memphis in 1977 before being signed by Miles Copeland III to the young I.R.S.

The ensuing court case prevented them from releasing anything until 1983, when they recorded Smell of Female live at New York's Peppermint Lounge; Kid Congo Powers subsequently departed.

Mike Metoff of the Pagans (cousin of Nick Knox) was the final second guitarist – albeit only live – of the Cramps' pre-bass era.

With the release of 1986's A Date With Elvis, the Cramps permanently added a bass guitar to the mix, but had trouble finding a suitable player, so Ivy temporarily filled in as the band's bassist.

Each night of the tour opened with the band coming on one at a time each: Knox, Fur, Ivy and then Lux before launching into their take on Elvis' "Heartbreak Hotel".

The album featured what was to become a predominating theme of their work from here on: a move away from the B-movie horror focus to an increased emphasis on sexual double entendre.

The album met with differing fates on either side of the Atlantic: in Europe, it sold over 250,000 copies, while in the U.S. the band had difficulty finding a record company prepared to release it until 1990.

The Cramps hit the Top 40 in the UK for the first and only time with "Bikini Girls with Machine Guns";[4] Ivy posed as such both on the cover of the single and in the promotional video for the song.

That same year, Lux Interior did a voiceover for the lead singer character of the band The Bird Brains on the animated TV show SpongeBob SquarePants singing 'Underwater Sun.'

On February 4, 2009, Lux Interior died at the Glendale Memorial Hospital after suffering an aortic dissection which, contrary to initial reports about a pre-existing condition, was "sudden, shocking and unexpected".

Their sound was heavily influenced by early rockabilly, such as Jerry Lott AKA The Phantom, whose 1958 single 'Love Me' they covered,[13] rhythm and blues, and rock and roll like Link Wray and Hasil Adkins, 1960s surf music acts[14] such as the Ventures and Dick Dale, 1960s garage rock artists like the Standells, the Trashmen, the Green Fuz and the Sonics, as well as the post-glam/early punk scene from which they emerged, as well as citing Ricky Nelson as being an influence during numerous interviews.

[12][19] The term "psychobilly" was first used in the lyrics to the country song "One Piece at a Time", written by Wayne Kemp for Johnny Cash, which was a Top 10 hit in the United States in 1976.

"[19] The Cramps have since rejected the idea of being a part of a psychobilly subculture, noting that "We weren't even describing the music when we put 'psychobilly' on our old fliers; we were just using carny terms to drum up business.

[29] The Cramps have been cited as an influence by musicians including 45 Grave,[33] the Nomads,[34] Zombina and the Skeletones,[35] Inca Babies,[36] Creeper,[37] the Black Keys,[38] the White Stripes,[39] the Sisters of Mercy,[40] My Bloody Valentine,[41] Faith No More[42] and Southern Culture on the Skids.