This review is focused on understanding of the charge-transport physics of high-mobility organic semiconductors at a molecular level. We review recent high-mobility small-molecule and conjugated polymer materials with a focus on crystalline materials that have been able to exceed mobilities of 0.5-1 cm 2 /V s. We discuss some of the main, competing factors that govern charge transport in these materials and present theoretical approaches that have been developed to describe systems in which moderately strong intermolecular electronic interactions and strong electron-phonon interactions are present. Finally, we review recent experimental results that have aimed to address the important question of whether at room-temperature charge carriers in these high-mobility organic semiconductors are in fact simply extended Bloch electrons that undergo occasional scattering processes or are localized on individual molecules and move by hopping. 1 Introduction There has been tremendous progress in discovering new classes of organic semiconductors, that provide field-effect mobilities, m, above 1 cm 2 /V s and allow addressing increasingly demanding thin-film electronic applications [1]. For many years, the performance of organic field-effect transistors (OFETs) seemed to be inherently lower than that of their inorganic counterparts, in particular, compared to amorphous silicon (a-Si) and polycrystalline FETs which have characteristic mobilities of the order of 0.5-1 and 100 cm 2 /V s, respectively. Due to extensive materials development and evaluation of different classes of organic semiconductors there is now a broad range of organic semiconductors, both vacuum and solution processible, as well as small-molecule and conjugated polymer based, which are able to reach mobility values exceeding that of a-Si. The processing characteristics of these materials make them suitable for applications that cannot easily be addressed by many inorganic materials. Organic semiconductors are inherently low-temperature materials. Because of the absence of covalent bonding between molecules, they can be processed at temperatures below typically 100-150 8C