In the present paper we consider the band structure and the Davydov splitting of the first triplet exciton states in crystalline naphthalene, anthracene, and biphenyl. It is found that: (a) An important contribution to the triplet exciton bandwidth arises from intermolecular exchange interaction. These interactions are calculated in the molecular orbital π-electron approximation, (b) Excitation exchange effects due to spinorbit coupling are negligible, (c) Nonorthogonality corrections, considered within the framework of the symmetric orthogonalization procedure, have been found to be small, (d) Crystal-field mixing of triplet states arising from π-π* excitations has no effect on the triplet bands, (e) An important contribution to the triplet exciton bandwidth may arise from configuration interaction with charge-transfer states. The dynamics of triplet excitons in aromatic crystals was studied in the two limiting cases of strong and weak scattering. The band model, with the constant mean-free-path approximation, leads to a mean free path of the order of one to two lattice distances and seems to be inappropriate. Triplet-triplet annihilation leading to delayed blue fluorescence in crystalline anthracene can be adequately described in terms of a random-walk diffusion model when the effects of charge-transfer interactions are included.