Abstract Organic electrochemical transistors (OECTs) are thin-film transistors that have shown great promise in a range of applications including biosensing, logic circuits, and neuromorphic engineering. The device physics of OECTs are determined by the interaction between ionic and electronic charge carriers. This interaction sets OECTs apart from conventional transistor technologies and has necessitated the development of device models for the unique behavior of OECTs. In this Review, we discuss existing models for OECTs and provide a framework for understanding these models. Moreover, we show how the insight from these models inform device optimization. Finally, we discuss details of OECT operation that are not well-understood and that provide exciting opportunities for future research. Graphical abstract Image Highlights • Review article on device physics of organic electrochemical transistors. • Geometry scaling for response time and transconductance. • Understanding ionic/electronic mixed conduction. • Design strategies for mitigation of parasitic resistance. • Density of states influence on charge transport. [ABSTRACT FROM AUTHOR]