We describe physically based analytical models for n-channel a-Si:H Thin Film Transistors (TFTs) and for n- and p-channel polysilicon TFTs. The models cover all regimes of transistor operation: leakage, subthreshold, above threshold conduction, and the kink regime in polysilicon TFTs. The models contain a minimum number of parameters which are easily extracted and can be readily related to the structural and material properties of the TFTs. The models have been verified for a large number of devices to scale properly with device geometry. Both models and accompanying automatic parameter extraction software are available over the internet.