Singlet fission, in which an initially excited singlet state spontaneously splits into a pair of triplet excitons, is a process that can potentially boost the efficiency of solar energy conversion. The separate electronic bands in organic semiconductors make them especially useful for dividing a high-energy singlet exciton into a pair of lower-energy triplet excitons. Recent experiments illustrate the role of spin coherence in fission, while kinetic models are used to describe how triplet and singlet states interact on longer time scales. Despite insights gained from recent experiments, the detailed structure and dynamics of the electronic states involved in the initial step of singlet fission remain active areas of investigation. On longer time scales, finding ways to efficiently harvest the triplet excitons will be an important challenge for making devices based on this phenomenon. A full understanding of singlet fission requires consideration of a sequence of photophysical events (decoherence, relaxation, and diffusion) occurring on different time scales.