This paper summarized the advances in two transverse models for nonlinear vibration of axially moving beams. Based on a nonlinear model for planar vibration of axially moving beams with coupled transverse and longitudinal motion, the derivation of two nonlinear models of transverse vibration was reviewed. The comparisons between approximate analytical results based on the two models for free, forced and parametric vibration of axially moving beams were surveyed. The deviations of the numerical solutions to the two transverse models from the solution to the coupled equation for different vibrations were also summarized. Some problems for further investigations were discussed.