As naturalised children of immigrants from the Caribbean, part of the aftermath of World War II, the "kids" were moved to London. They attended a local high school near Ladbroke Grove.

The original members of Aswad were Brinsley Forde, George Oban, Angus "Drummie Zeb" Gaye, and Donald Griffiths. Courtney Hemmings was a frequent contributor in the 1970s, including as part of the backing band on Burning Spear's 1977 Live album, recorded at the Rainbow Theatre in London. Other contributors included Vin Gordon, Bongo Levi, and Karl Pitterson.

They became one the UK's top reggae bands with songs, typical of the time, about the oppression of black youth, such as "Three Babylon" and "It's Not Our Wish", and the powerful jazz-influenced instrumental "Warrior Charge" (full versions of these available on the Showcase album).

Aswad gained a wider audience with the New Chapter album (1981). "Love Fire" gained wide recognition when it was used as the backing rhythm for Dennis Brown's "Promised Land".

Among Aswad's catalogue of hits is "Don't Turn Around", a UK no.1 pop hit in 1988. This track was originally a B-side to Tina Turner's hit "Typical Male", which was later covered by Ace of Base; they followed this up with UK #11 hit "Give A Little Love", and a reggae flavoured rendition of "Best of My Love", first popularised and written by The Eagles.

Their next hit, Shine, was released in 1994. Another track was the upbeat 1998 remake of The Police's "Invisible Sun", performed with Sting.

The band also hold the distinction of having played with each one of the ex-Wailers.