The Rats were formed in Dun Laoghaire, near Dublin, Ireland, in 1975 by Geldof (born Robert Frederick Zenon Geldof, October 5, 1954, Dun Laoghaire, Ireland), a former journalist; Johnnie Fingers (keyboards); Gerry Cott (guitar); Garry Roberts (guitar); Pete Briquette (bass); and Simon Crowe (drums). They took their name from Woody Guthrie's novel Bound for Glory. The group moved to London in October 1976, and became associated with the punk rock movement. Signing to Ensign Records, they released their debut single, "Lookin' After No. 1," in August 1977. It was the first of nine straight singles to make the U.K. Top 40.

Their debut album, The Boomtown Rats, was released in September 1977, on Ensign in the U.K. and on Mercury in the U.S. Their second album, Tonic for the Troops, appeared in June 1978 in the U.K., along with their first U.K. Top Ten hit, "Like Clockwork." In the fall, "Rat Trap" from the album hit number one. A Tonic for the Troops was released in the U.S. on Columbia Records in February 1979 with two tracks from The Boomtown Rats substituted for tracks on the U.K. version.

The Boomtown Rats' second straight U.K. number one came in the summer of 1979 with "I Don't Like Mondays," a song inspired by a California teenager who had gone on a killing spree and glibly justified her action with the title line. It was contained on the Rats' third album, The Fine Art of Surfacing, released in October 1979, and subsequently became the band's only U.S. singles-chart entry. The album also contained their next U.K. Top Ten hit, "Someone's Looking at You."

The Boomtown Rats released their final U.K. Top Ten hit, "Banana Republic," in November 1980, followed by their fourth album, Mondo Bongo, in January 1981. At this point, guitarist Gerry Cott left the group, and they continued as a quintet. Their fifth album, V Deep, was released in the U.K. in February 1982. In the U.S., Columbia initially released only a four-song EP drawn from the album The Boomtown Rats, finally releasing the full LP in September, when it failed to chart. Also in 1982, Geldof starred in the movie Pink Floyd: The Wall.

Columbia released the six-song compilation Ratrospective in March 1983, but rejected the band's newly recorded sixth album, In the Long Grass, which was released by Ensign in England. In 1984, Geldof and Midge Ure wrote "Do They Know It's Christmas?" and organized the star-studded Band Aid group to record it for Ethiopian relief, resulting in the biggest selling single in U.K. history. Geldof then went on to organize the two Live Aid concerts, held on July 13, 1985, in London and Philadelphia. Geldof's increased visibility led to the belated U.S. release of In the Long Grass, but when it failed to chart, the Boomtown Rats were left without a record label. The group folded in 1986, and Geldof launched a solo career.