Singlet fission, the splitting of a singlet exciton into two triplet excitons in molecular materials, is interesting not only as a model many-electron problem, but also as a process with potential applications in solar energy conversion. Here we discuss limitations of the conventional four-electron and molecular dimer model in describing singlet fission in crystalline organic semiconductors, such as pentacene and tetracene. We emphasize the need to consider electronic delocalization, which is responsible for the decisive role played by the Mott-Wannier exciton, also called the charge transfer (CT) exciton, in mediating singlet fission. At the strong electronic coupling limit, the initial excitation creates a quantum superposition of singlet, CT, and triplet-pair states, and we present experimental evidence for this interpretation. We also discuss the most recent attempts at translating this mechanistic understanding into design principles for CT state-mediated intramolecular singlet fission in oligomers and polymers.