Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an original regim
e of transport called textit{transient localization}, sharing features of both localized and itinerant electron systems. After a brief review of experimental observations that pose a challenge to the theory, we concentrate on a commonly studied model which describes the interaction of the charge carriers with inter-molecular vibrations. We present different theoretical approaches that have been applied to the problem in the past, and then turn to more modern approaches that are able to capture the key microscopic phenomenon at the origin of the puzzling experimental observations, i.e. the quantum localization of the electronic wavefuntion at timescales shorter than the typical molecular motions. We describe in particular a relaxation time approximation which clarifies how the transient localization due to dynamical molecular motions relates to the Anderson localization realized for static disorder, and allows us to devise strategies to improve the mobility of actual compounds. The relevance of the transient localization scenario to other classes of systems is briefly discussed.
