The performance of organic based field-effect transistors (FETs) has recently known significant improvements. The mobility of organic FETs now approaches 1 cm 2 V –1 s –1 with short molecules, and 0.1 cm 2 V –1 s –1 with polymers. Here, we review recent results on these devices. Attention is paid to the models developed to account for charge transport in organic semiconductors, which present significant differences from their inorganic counterparts. In particular, the mobility is gate bias dependent, which actually mirrors a dependence of the mobility on charge concentration. This has been explained in terms of trap limited transport. The temperature dependence of the mobility is usually thermally activated, which is also consistent with trap limited transport, but could also be explained by a mechanism of small polaron hopping. Furthermore, recent measurements show that the mobility can become temperature independent, which could open the way to further improvements of the performance of organic transistors.