A model for carrier velocity and velocity saturation in amorphous metal oxide thin-film transistors (TFTs) is presented and discussed. The charge transport in such TFTs involves the interplay between the trapping and extended state transport when the mobility is large enough. The model considers multiple trapping and release and band transport between the trapping events. The dominant scattering mechanisms are polar optical phonon scattering and trapped carrier scattering. Our model predicts that the velocity will saturate due to emission of optical phonons at high electric fields (>105 V/cm) with a maximum value near 107 cm/s. Trapping reduces the velocity and also imparts an additional electric field dependence in which the velocity increases with field. The model is compared with the experimental data from several groups. Experimental data are strongly affected by contact resistance effects, which must be corrected for. Procedures to correct for the contact resistance are described. The corrected velocity-field characteristics of six amorphous indium gallium zinc oxide (IGZO) TFTs are presented.