The inversion field-effect transistor is the basic device of modern microelectronics and is nowadays used more than a billion times on every state-of-the-art computer chip. In the future, this rigid technology will be complemented by flexible electronics produced at extremely low cost. Organic field-effect transistors have the potential to be the basic device for flexible electronics, but still need much improvement. In particular, despite more than 20 years of research, organic inversion mode transistors have not been reported so far. Here we discuss the first realization of organic inversion transistors and the optimization of organic depletion transistors by our organic doping technology. We show that the transistor parameters--in particular, the threshold voltage and the ON/OFF ratio--can be controlled by the doping concentration and the thickness of the transistor channel. Injection of minority carriers into the doped transistor channel is achieved by doped contacts, which allows forming an inversion layer.