Ismailism is defined by a parting from the rest of Shiism at a single point, and then by a series of further partings of its own.
The sixth Imam, Jafar al-Sadiq, died in 765. His son Ismail had predeceased him or been set aside, the accounts differ, and this is genuinely contested rather than merely uncertain, and the majority followed another son, Musa al-Kazim, whose line the Twelvers count to the twelfth. A minority held that the designation of Ismail could not be revoked and followed his line instead. From that come the Ismailis.
What distinguishes them theologically is the systematic distinction between zahir and batin, the outer form of scripture and law and its inner meaning. The inner meaning is unfolded by the Imam, which makes interpretation dependent on a living authority rather than on scholarly consensus. Ismaili thought absorbed a great deal of Neoplatonic philosophy, and its theology is markedly negative: God is beyond attribution altogether, beyond being and non-being, and cannot be described.
Politically the movement was formidable. The Fatimid Caliphate, founded in North Africa in 909 and ruling Egypt from 969, was an Ismaili state that built Cairo and founded al-Azhar, and for two centuries it was a genuine rival to Baghdad. Its collapse in 1171 scattered the tradition.
The later Nizari community centred on the fortress of Alamut in Persia is the source of the word assassin, which entered European languages through crusader reports and a false etymology involving hashish. The killings were real and were a deliberate strategy of a small state against much larger ones; the drug story is a legend, and the modern community regards the label as a slander that has followed it for eight centuries.