Thin-film transistors (TFTs) have grown into a huge industry due to their broad applications in display, radio-frequency identification tags (RFID), logical calculation, etc. In order to bridge the gap between the fabrication process and the circuit design, compact model plays an indispensable role in the development and application of TFTs. The purpose of this review is to provide a theoretical description of compact models of TFTs with different active layers, such as polysilicon, amorphous silicon, organic and In-Ga-Zn-O (IGZO) semiconductors. Special attention is paid to the surface-potential-based compact models of silicon-based TFTs. With the understanding of both the charge transport characteristics and the requirement of TFTs in organic and IGZO TFTs, we have proposed the surface-potential-based compact models and the parameter extraction techniques. The proposed models can provide accurate circuit-level performance prediction and RFID circuit design, and pass the Gummel symmetry test (GST). Finally; the outlook on the compact models of TFTs is briefly discussed.