We present an overview of recent studies of the charge transport in the field effect transistors on the surface of single crystals of organic low-molecular-weight materials. We first discuss in detail the technological progress that has made these investigations possible. Particular attention is devoted to the growth and characterization of single crystals of organic materials and to different techniques that have been developed for device fabrication. We then concentrate on the measurements of the electrical characteristics. In most cases, these characteristics are highly reproducible and demonstrate the quality of the single crystal transistors. Particularly noticeable are the small sub-threshold slope, the non-monotonic temperature dependence of the mobility, and its weak dependence on the gate voltage. In the best rubrene transistors, room-temperature values of $μ$ as high as 15 cm$^2$/Vs have been observed. This represents an order-of-magnitude increase with respect to the highest mobility previously reported for organic thin film transistors. In addition, the highest-quality single-crystal devices exhibit a significant anisotropy of the conduction properties with respect to the crystallographic direction. These observations indicate that the field effect transistors fabricated on single crystals are suitable for the study of the \textit{intrinsic} electronic properties of organic molecular semiconductors. We conclude by indicating some directions in which near-future work should focus to progress further in this rapidly evolving area of research.

Review article, to appear in special issue of Phys. Stat. Sol. on organic semiconductors