Organic field-effect transistors (OFETs) have been the hotspot in information science for many years as the most fundamental building blocks for state-of-the-art organic electronics. During the field-effect modulation of the semiconducting channel, the gate dielectric always has a significant influence on the charge transport behaviours. Hence, understanding of the nature of charge carriers at the semiconductor/dielectric interface and realizing functional OFETs with superior performance have been the cornerstones for the sustainable advancement in organic electronics. With the joint efforts of predecessors, various basic theories and models have been advanced to describe the charge transport processes in organic crystals. To make a further breakthrough, more accurate correlation between the electrostatic properties of dielectrics and charge carrier behaviours is urgently needed. The high-quality interface-like films, without nonideal factors, two-dimensional molecular crystals (2DMCs), have been spotted as a powerful platform for direct and accurate characterization of the intrinsic charge transport behaviours at the semiconductor/dielectric interface. In this article, the recent breakthroughs in the physics of charge transport, interfacial effects, and perspectives with 2DMCs in OFETs are reviewed, providing great benefits to penetrate the fundamental studies and keep up with the revolutionary advancement in organic-electronics road map.