  The gravitational interaction between a protoplanetary disc and planetary
sized bodies that form within it leads to the exchange of angular momentum,
resulting in migration of the planets and possible gap formation in the disc
for more massive planets. In this article, we review the basic theory of
disc-planet interactions, and discuss the results of recent numerical
simulations of planets embedded in protoplanetary discs. We consider the
migration of low mass planets and recent developments in our understanding of
so-called type I migration when a fuller treatment of the disc thermodynamics
is included. We discuss the runaway migration of intermediate mass planets
(so-called type III migration), and the migration of giant planets (type II
migration) and the associated gap formation in the disc. The availability of
high performance computing facilities has enabled global simulations of
magnetised, turbulent discs to be computed, and we discuss recent results for
both low and high mass planets embedded in such discs.
