This review presents an overview of the recent progress made in the field of carbon nanotube (CNT)-based field-effect transistors (FETs). Starting from the simplest device architectures, various methods reported for fabricating CNT-FETs are presented. The main focus is laid on the use of chemical functionalization strategies both at a tube and at a device level to improve the performance of the devices. In addition to solid dielectric gate insulators, the use of liquids or solid polymer electrolytes as effective electrochemical gating media is outlined. Following this, device parameters of the various CNT-FETs are compared and discussed. Finally, the utility of scanning photocurrent microscopy as an efficient characterization tool to estimate electronic band-profiles of CNT-FETs is highlighted. The review concludes with future perspectives in this rapidly emerging field.