A number of breakthroughs occurred in last years in studies of excitons in semiconductors. The ⌠Rydberg■ excitons with principle quantum numbers ~20 have been discovered in cuprous oxide, the excitons in novel two-dimensional systems - transition metal dichalcogenides and stacking faults in GaAs - have been observed, studies of spin-dependent excitonic transport have also became topical. The spin-orbit and exchange interactions, which define the fine structure of the electron-hole pair energy levels and control the exciton dynamics, play an important role in these systems. The theory of the exciton states fine structure is presented in the talk and the manifestations of the fine structure in optical and transport properties of excitons are analyzed. The spin and valley dynamics of two-dimensional excitons is discussed. It is shown that the fine structure of exciton states drastically affects the exciton transport via coherent scattering effects. It is demonstrated that depending on the relation between the spin-orbit and exchange splittings of the excitonic levels, interference of excitons on the closed loops can result in their weak localization or antilocalization.