Described simply, singlet fission is a process in which a singlet excited molecule transfers about half of its excitation energy to a neighbor molecule, both end up in their triplet state, and the two triplet excitations diffuse apart. The process is of interest for solar cells. Used in conjunction with ordinary solar cell material, a layer of singlet-fission material offers an opportunity to utilize higher energy photons more efficiently. The maximum theoretical efficiency is then close to 1/2 instead of the Shockley-Queisser value of 1/3 that applies to an ordinary single-junction cell. The problem that prevents an immediate production of singlet fission solar cells is the dearth of sufficiently stable efficient materials. The formulation of simple rules for the design of suitable compounds for the purpose is discussed.