Small-molecule organic semiconductors, together with polymers, form the basis for the emerging field of organic electronics. Despite the rapid technological progress in this area, our understanding of fundamental electronic properties of these materials remains limited. Recently developed organic field-effect transistors (OFETs) based on single crystals of small-molecule organic materials are characterized by an unprecedented quality and reproducibility. These devices provide a unique tool to study the fundamentals of polaronic transport on organic surfaces and to explore the limits of OFET performance. This Colloquium focuses on the intrinsic, not limited by static disorder, charge transport in single-crystal OFETs and on the nature of defects on surfaces of organic crystals. In the conclusion, an outline of the outstanding problems that are now becoming within experimental reach owing to the development of single-crystal OFETs is presented.