The photophysical behavior of organic semiconductors is governed by their excitonic states. In this review, I classify the three different exciton types (Frenkel singlet, Frenkel triplet, and charge transfer) typically encountered in organic semiconductors. Experimental challenges that arise in the study of solid-state organic systems are discussed. The steady-state spectroscopy of intermolecular delocalized Frenkel excitons is described, using crystalline tetracene as an example. I consider the problem of a localized exciton diffusing in a disordered matrix in detail, and experimental results on conjugated polymers and model systems suggest that energetic disorder leads to subdiffusive motion. Multiexciton processes such as singlet fission and triplet fusion are described, emphasizing the role of spin state coherence and magnetic fields in studying singlet ↔ triplet pair interconversion. Singlet fission provides an example of how all three types of excitons (triplet, singlet, and charge transfer) may interact to produce useful phenomena for applications such as solar energy conversion.