The known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary disks provides one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure and physical processes that drive the evolution of the protoplanetary disk. In this review we focus on how disk-planet interactions drive the migration of planets when different assumptions are made about the physics of angular momentum transport, and how it drives accretion flows in protoplanetary disk models. In particular, we consider migration in discs where: (i) accretion flows arise because turbulence diffusively transports angular momentum; (ii) laminar accretion flows are confined to thin, ionised layers near disk surfaces and are driven by the launching of magneto-centrifugal winds, with the midplane being completely inert; (iii) laminar accretion flows pervade the full column density of the disc, and are driven by a combination of large scale horizontal and vertical magnetic fields.
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