Many advanced materials have been developed for organic field-effect transistors (OFETs) or thin-film transistors (TFTs) based on organic and organic hybrid materials. However, although many new OFETs exhibit superior characteristic parameters (such as high mobility), most of them show nonideal performances that have strongly limited progress in the design of molecules, the understanding of transport mechanisms, and the circuit applications of OFETs. In this review, the device physics of ideal and nonideal OFETs is discussed first to understand the factors that limit effective mobility in semiconducting channels, distort the potential distribution, or reduce the drift electric field. Then, recent advances in optimizing the material combinations, device structures, and fabrications of OFETs toward ideal transistors are discussed. Based on the good control of materials and interfaces, some new and novel concepts to utilize the nonideal properties of OFETs to build low-power circuits and integrated sensors are also discussed.