Divinyls formed in 1980, founded by Mark McEntee and fronted by lead singer Chrissy Amphlett. After scoring several gigs, they were discovered by Australian director Ken Cameron. This led to Divinyls providing the entire soundtrack for his 1982 film Monkey Grip. Amphlett was also given a supporting role in the film, playing a temperamental rock singer loosely based on herself, fronting a band played by other Divinyls members. In the film, the band performed their debut single "Boys in Town", as well as other songs "Only Lonely", "Elsie", "Only You", "Girlfriends" and "Gonna Get You", the latter being the first appearance of them in the film. The soundtrack Music from Monkey Grip was acknowledged as a Divinyls album, and when released in 1982, it made the top twenty-five of the Australian Albums Chart.
"Boys in Town" was a success in Australia where it made the top ten, peaking at number eight in 1981. The next year "Science Fiction" was released and was also a success, peaking at number thirteen. When Desperate was released, it climbed the albums chart and eventually peaked at number five. In addition, it proved to be among the top twenty most successful albums of 1983, ranking in at number seventeen according to the Kent Music Report end of year chart.
The track listing of Desperate differed between the Australian release and the international version. Because Divinyls had already released the Monkey Grip soundtrack, which contained the songs performed in the film, in particular the single "Boys in Town", they were not included on the original Australian release of Desperate. This meant that "Science Fiction" was released as the official lead single. On the international release of Desperate, some of the songs from the Monkey Grip soundtrack were included as official album tracks, such as "Boys in Town", "Only Lonely", "Only You" and "Elsie".
The majority of the songs on Desperate were written by Amphlett and/or McEntee except "Siren (Never Let You Go)", which was written by band member Bjarne Ohlin, and "I'll Make You Happy", which was a cover of the original 1966 song by The Easybeats.
Caroline Records announced that a remastered CD version of the international version of Desperate album was released on 5 February 2008.