Explaining the diversity of orbital architectures displayed by the known exoplanet population is one of the major challenges confronting theories of planet formation. Gravitational interactions between young planets and their protoplanetary disks provide one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure of the protoplanetary disk and the physical processes that drive disk evolution. In this review, we focus on recent developments showing how migration changes when different assumptions are made about the processes responsible for driving the accretion of gas through the disk onto the star (e.g., turbulent viscosity versus magnetized winds), and how migration is modified when a simplified treatment of the thermal evolution of the disk is replaced by more sophisticated approaches that include radiation transport.