Craig's group Culture Club became one of the most successful bands of the 1980s, selling millions of albums. In 1988, he released a solo single entitled "I'm a Believer", which failed to make an impact.
Craig was an executive producer, in the mid-1990s, for his own dance label, SLAMM records, generating dance hits by artists like Mr. & Mrs. Smith and Mankey.
Craig went to St Clement Danes School in DuCane Road, Hammersmith. Craig had two children with Cleo Scott (daughter of the author and political campaigner Erin Pizzey), a son, Keita, born in 1977 and a daughter Amber, born 18 months later. Keita was a paranoid schizophrenic who committed suicide in Wandsworth Prison in 2000. Craig ended his relationship with Cleo Scott shortly after Culture Club's rise to fame in 1982. He is now married to an Italian woman named Lilli and they have three sons: Milo Emile, the footballer Paco Gigi, and Geo Luca.