C. Baruteau (University of Cambridge, DAMTP, United Kingdom),
A. Crida (Observatoire de la Cote d'Azur, Nice, France),
B. Bitsch (Observatoire de la Cote d'Azur, Nice, France),
J. Guilet (University of Cambridge, DAMTP, United Kingdom),
S.-J. Paardekooper (University of Cambridge, DAMTP, United Kingdom),
F. Masset (UNAM, Instituto de Ciencias Fisicas, Mexico),
R. Nelson (Queen Mary, University of London, Astronomy unit, United Kingdom),
W. Kley (Universitat Tübingen, Institut für Astronomie & Astrophysik, Germany),
J. Papaloizou (University of Cambridge, DAMTP, United Kingdom)

The great diversity of extrasolar planetary systems has challenged our understanding of how planets form, and how their orbits evolve as they form. Among the various processes that may account for this diversity, the gravitational interaction between planets and their parent protoplanetary disc plays an inevitable role in shaping young planetary systems by causing considerable mobility. Planet-disc forces are large, and the characteristic times for the evolution of planets orbital elements are much shorter than the lifetime of protoplanetary discs. The determination of such forces is difficult, because it involves many physical mechanisms and it requires a detailed knowledge of the disc structure. The intense research of the past few years, with the exploration of many new avenues, represents a very significant improvement on the state of the discipline presented in PPV. The objective of this chapter is to review current understanding of planet-disc interactions. Emphasis is placed on mechanisms capable of slowing down, stalling or reversing planet migration, which may help account for the exoplanets diversity. We then address how well global models of planet formation and migration are able to match observations of extrasolar planets.

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