Singlet fission is a spin-allowed process, unique to molecular photophysics, whereby one singlet excited state is converted into two triplet states. The phenomenon has been observed in molecular crystals, aggregates, disordered thin films, and covalently-linked dimers, where the chromophores are oriented such that the electronic coupling between singlet and the double triplet states is large. Being spin allowed, the process can occur very rapidly (on a picosecond or femtosecond timescale) and out-compete radiative decay (that generally occurs on a nanosecond timescale) thereby producing two triplets with very high efficiency. The process is distinct from intersystem crossing, in that singlet fission does not involve a spin flip, but is mediated by two triplets coupled into an overall singlet. It has been proposed that singlet fission in organic photovoltaic devices could improve the photoconversion efficiencies.