  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 $\mu$ 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.
