Although he was born just north of the Windy City, Branch grew up in Los Angeles, only to return to Chicago in 1969 to attend the University of Illinois. Spurred on by the entrancing riffs of mouth-organ masters Carey Bell, Big Walter Horton, and Junior Wells, Branch began to make a name for himself. He replaced Bell in Willie Dixon's Chicago Blues All-Stars, recording with the prolific legend and touring extensively.

The SOBs really were dominated by second-generation talent at the start -- guitarist Lurrie Bell was Carey Bell's son, while bassist Freddie Dixon was the offspring of Willie Dixon. They contributed three tunes to Alligator's first batch of Living Chicago Blues anthologies in 1978. The SOBs waxed Where's My Money?, their Red Beans Records LP, in 1984; by then, personnel included guitarist Carlos Johnson, bassist J.W. Williams, and drummer Moses Rutues. Shortly after that album was completed, guitarist Carl Weathersby was installed as co-frontman, where he remains (as does Rutues; bass is now handled by Nick Charles).

Other than co-headlining Alligator's 1990 summit meeting Harp Attack! with fellow harp masters Junior Wells, Carey Bell, and James Cotton, Branch largely busied himself with extensive sideman work (he's first-call session harpist around the Windy City) and teaching an innovative "Blues in the Schools" program until 1995. Verve issued his The Blues Keep Following Me Around, an impressive showcase for his gravelly vocals and spellbinding harp. Satisfy Me followed in 1999. Chicago's Young Blues Generation was issued on Evidence in 2001.