Named after Ismail bin Jafar, who they believe to be the seventh Imam, rather than the lineage accepted by Ithna'sheri (Twelver) Shi'a.
The rulers of the medieval Fatimid dynasty based in Cairo, Egypt, were Ismaili.
There are several sub-groups, the largest (and best known in the west) being perhaps the Nizari line, who accept the Aga Khan as their spiritual leader.