  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 regime 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.
