This dissertation describes our study of a photophysical process that leads to ultrafast generation of triplet excitons following photoexcitation, singlet exciton fission, in three different acene dimers and diradicaloids. In pentacene and tetracene dimers, we investigate their mechanism of singlet fission. In a series of diradicaloids, we study the relation between molecular structure, diradical character and the suitability for singlet fission. In the first two chapters we explore singlet fission in pentacene dimer. We demonstrate fast and highly efficient intramolecular singlet fission, consisting of two covalently attached pentacene units. The singlet fission pathway is governed by the energy gap between singlet and charge-transfer states, which change dynamically with molecular geometry but are primarily set by the side group. The process exhibits a sensitivity to solvent polarity and competes with geometric relaxation in the singlet state, while subsequent triplet decay is strongly dependent on conformational freedom. The near orthogonal arrangement of the pentacene units is unlike any structure currently proposed for efficient singlet fission and points toward new molecular design rules. Furthermore, these results are the first to demonstrate the role of charge-transfer states in singlet fission and highlight the importance of solubilising groups to optimise excited-state photophysics. In the next chapter, we examine singlet fission in tetracene dimer, where singlet fission is energetically unfavourable. We demonstrate triplet yield as high as 190% can be achieved via fission from higher singlet excited states mediated by charge-transfer states. The outcomes of this study provide deeper insight into the role of hot singlet states in singlet fission and point toward less stringent molecular design rules. In the last chapter, we shift our focus on a new class of molecules, diradicaloid molecules. We explore a family of zethrene molecules, with tuneable diradical character, and demonstrate their general ability to undergo rapid singlet fission via spin-entangled and emissive triplet-pair state TT. A wide range of zethrene molecules are found to be suitable for singlet fission, with additional benefits of high absorption coefficients and photo-/chemical stability.