The first thing to say about Alevism is that what it is remains genuinely contested, including among Alevis, and that the dispute is not academic: it determines whether Alevi places of worship are recognised in Turkish law.
Three positions are held. That Alevism is a branch of Shia Islam, deriving from Twelver veneration of Ali and the Twelve Imams with Sufi and older Anatolian elements. That it is a distinct heterodox Anatolian Islam, not reducible to either Sunni or Shia. And, argued by a substantial segment of Alevis themselves, that it is a religion in its own right and not Islam at all. Sunni orthodoxy has historically read it as heresy.
What can be described without settling the question is the practice and the theology. Alevism venerates Ali intensely, and the formula of Allah, Muhammad and Ali is understood as a manifestation of light rather than as three persons. Its central theological idea is Insan-i Kamil, the perfect human, and the divine is sought within the person rather than in a law imposed from outside. It does not observe the five daily prayers, does not fast in Ramadan in the Sunni manner, does not require the pilgrimage, and does not worship in mosques. The prohibition on alcohol is not generally observed.
Its emergence is placed in Anatolia among Turkic populations who received Islam from wandering dervishes rather than from urban scholars, consolidating around Haji Bektash Veli and, in Ottoman times, the Bektashi order, which supplied the Janissary corps with its chaplains until that corps was destroyed in 1826.