A multi-phase transport (AMPT) model was constructed to provide a self-contained kinetic theory-based description of relativistic nuclear collisions. Since the transport model approach can address not only equilibrium dynamics but also non-equilibrium dynamics, it is well suited to study the transition of nuclear collisions from the dilute limit to the hydrodynamic limit. Here I will review several model developments that have been carried out in recent years. They include the incorporation of modern parton distribution functions of nuclei for high energy heavy ion collisions, improvement of heavy quark productions, local nuclear scaling of two key input parameters for self-consistent system size dependence and centrality dependence, and improvements of the parton cascade.