The group's initial incarnation, founded by Jones and film director Don Letts once played in Basement 5 (maker of The Punk Rock Movie, various Clash music videos, and later the Clash documentary Westway to the World), debuted with the 1985 release This Is Big Audio Dynamite. 1986's No. 10, Upping St. reunited Jones for one album with former Clash-mate Joe Strummer who co-produced the album and co-wrote a number of songs, but that reacquaintance soon ended. BAD supported U2 on their 1987 world tour, then followed with 1988's Tighten Up Vol. '88 and 1989 Megatop Phoenix. BAD supported U2 on the leg of their 1992 Zoo TV Tour that included Australia, New Zealand and Japan.
Jones' latest projects include work with The Libertines and his own outlet with Tony James of Sigue Sigue Sputnik fame - Carbon Silicon
From Wikipedia:Big Audio Dynamite (later known as Big Audio Dynamite II and Big Audio, and often abbreviated BAD) were a British musical group formed in 1984 by the ex-guitarist and singer of The Clash, Mick Jones. The group were noted for their effective mixture of varied musical styles, incorporating elements of punk rock, dance music, hip hop, reggae, and funk. BAD's one constant throughout frequent shifts in membership and musical direction was the vocals provided by Mick Jones.