The Drumming System has a great section on reggae drumming. Reggae music began in the late 1960’s in Jamaica. Bands such as Bob Marley and the Wailers, Steel Pulse, Inner Circle, and King Tubby were popular bands that brought reggae into the mainstream. Carlton Barrett was a drumming pioneer in this style. He played drums for Bob Marley and the Wailers.
Stewart Copeland, the drummer for The Police, described reggae drumming as everything being flipped (as if you woke up on the wrong side of the bed). The reason it sounds backwards is because the emphasis is on the upbeat (ands).
Reggae can be played straight or swung. Played straight, it has a solid eight note feel. When it is swung, it sounds more like a shuffle.