There are mutliple artists with this name:

1) Overkill formed in 1980 in New Jersey, as the first thrash band to hit the U.S.A. east coast, and by many is considered to be the first thrash band. They rose first as a cover band called Virgin Killers from the ashes of The Lubricunts which had been a project of Carlos “D.D.” Verni and Lee “Rat Skates” Kundrat. They recruited Bobby “Blitz” Ellsworth. Formerly a bassist as well as a vocalist, Bobby was recruited strictly as a vocalist for the band. By the end of 1980 the band re-branded themselves as Overkill and in 1981 they completed their first original songs which included Unleash The Beast Within, Overkill I: The Nightmare Begins and Raise the Dead. These thrash metal songs pre-date the formation Exodus, Anthrax, Metallica, and many others of the genre.

Their original unknown guitarist was replaced by Dan Spitz. When Dan left to go to Anthrax, he was replaced by the guitars of Bobby Gustafson and Rich Conte. After Rich's departure that same year, the band was left with a single guitarist, Bobby Gustafson.

With a long string of infamous live performances in New York City area clubs like L'Amours, Overkill established a reputation as a blue-collar, working man's band.

After the band released a self-financed demo, Power in Black in 1983 and the self-titled EP Overkill in 1984, Overkill had a breakthrough hit in 1985 with Feel the Fire, a crushing thrash album released on Megaforce Records (and re-released on Noise International in 1988). The self-proclaimed "Wrecking Crew" - originally consisting of vocalist Bobby "Blitz" Ellsworth, bassist Carlos “D.D.” Verni, guitarist Bobby Gustafson, and drummer Rat Skates – were on a tear, borrowing heavily from punk rock roots while adding a venomous crunch that allowed them to compete with groups like Testament, Anthrax, and Megadeth.

By the release of 1987's Taking Over, the band had inked a deal with Atlantic Records. This relationship would last 7 years.

1988's Under the Influence and 1989's The Years of Decay represent Overkill in their most popular. Bob “Sid” Falck would replace Rat Skates on drums to bring his own brutal percussive assault to Verni's already powerful rhythm section. The band had already established a rabid fan base with songs like Rotten to the Core and Hammerhead) as well as their infamous cover of D.O.A.'s Fuck You). New songs like Evil Never Dies and Hello From the Gutter would become Overkill mainstays as well. A video for "Hello from the Gutter" garnered much fan attention when it received play on MTV's "Headbangers Ball."

1991's Horrorscope would bring great changes for Overkill. Gustafson left the band to pursue other interests and their fan base wavered but, in his place, the band recruited two guitarists, Rob Cannevino and Merritt Gant (ex-Faith or Fear), making them a 5-piece engine of destruction.

1993's I Hear Black saw the departure of Sid Falck and the arrival of Tim Mallare, who would continue on with the band for over 13 years.

1994's Wide Fucking Open(W.F.O.) would be Overkill's final album with Atlantic, as they would release their first live album, Wrecking Your Neck, on Edel Records in 1995.

1996-1999 would see Overkill release 3 more full-length albums (Killing Kind their second and final album on the Edel label. Switching to Steamhammer label in late 1996 they proceeded to release From the Underground and Below, and Necroshine) as well as a collection of live tracks and fan favorites (Fuck You! And Then Some). In 1999 they release an album of cover tunes (Coverkill) with guitarists Joe Comeau (ex-Liege Lord, ex-Annihilator) and Sebastian Marino (ex-Anvil).

In 2000, Overkill released Bloodletting, adding guitarist Dave Linsk to the fray. The current Overkill lineup would be completed with the release of the live album Wrecking Everything and the addition of second guitarist Derek “Skull” Tailer in 2002.

Overkill released one of their most popular albums to date, Killbox 13, on Spitfire Records in 2003.

2005 saw a little more churn, with Tim Mallare being replaced by drummer Rob Lipnicki and the band once again switched labels, this time to Regain Records. The released ReliXIV later that year. An entirely self-produced album ReliXIV is a continuation of the Overkill legacy. As Blitz himself says: "This album is about performance versus process... The music on this record is a blend of our progression and our roots, where we're headed and where we've been. We're the real deal. We have a common ground with our fans, and this album is about what we know and feel."

In 2006, Overkill joined up with Dave Mustaine's Gigantour along with Arch Enemy and Opeth.

On yet another label, Bodog Music headed by two previous owners of Megaforce Records,Jonny and Marsha Zazula, the band released Immortalis in October, 2007.

Current Line-up:

Carlos “D.D.” Verni - since 1980 - Bass
Bobby “Blitz” Ellsworth - since 1980 - Vocals
Dave Linsk - since 2000 - Guitar
Rob Lipnicki - since 2005 - Drums
Derek “Skull” Tailer - since 2002 - Guitar

Past Members:
Dan spitz : 1980 – 1981 : Guitar
Rich Conte : 1981 : Guitar
Bobby Gustafson : 1981 – 1990: Guitar
Rob Cannavino : 1990 – 1995: Guitar
Merritt Gant : 1990 – 1995 : Guitar
Joe Comeau : 1995 – 1999 : Guitar
Sebastian Marino : 1995 – 2000 : Guitar
Lee “Rat Skates” Kundrat : 1980 – 1987 : Drums
Mark Archibole : Drums
Bob “Sid” Falck : 1987 to 1992 : Drums
Tim Mallare : 1992 – 2005 : Drums

Official Website

2) Overkill was a short-lived German heavy metal group forming in 1980 and splitting up in 1982 after releasing one demo.

3) Overkill was from The United Kingdom, started in 1977 and played a form of the 'New Wave of British Heavy Metal' (NWOBHM). They split up in 1983 after the surge of popularity waned in 1983.