Monolayers of transition metal dichalcogenides, namely, molybdenum and tungsten disulfides and diselenides demonstrate unusual optical properties related to the spin-valley locking effect. Particularly, excitation of monolayers by circularly polarized light selectively creates electron-hole pairs or excitons in non-equivalent valleys in momentum space, depending on the light helicity. This allows studying the inter-valley dynamics of charge carriers and Coulomb complexes by means of optical spectroscopy. Here, we present a concise review of the neutral exciton fine structure and its spin and valley dynamics in monolayers of transition metal dichalcogenides. It is demonstrated that the long-range exchange interaction between an electron and a hole in the exciton is an efficient mechanism for rapid mixing between bright excitons made of electron-hole pairs in different valleys. We discuss the physical origin of the long-range exchange interaction and outline its derivation in both the electrodynamical and k·p approaches. We further present a model of bright exciton spin dynamics driven by an interplay between the long-range exchange interaction and scattering. Finally, we discuss the application of the model to describe recent experimental data obtained by time-resolved photoluminescence and Kerr rotation techniques. Kerr rotation dynamics at T=4K for a σ⁺ and σ^- pump beam in WSe₂. Inset: Schematics of the optical selection rules of the excitons photogenerated from charge carriers in K_± valleys and their coupling induced by the long-range exchange interaction.