Ever since the discovery in 1995 of an object with half the mass of Jupiter in a four-day orbit around the star 51 Pegasi, it has been clear that the dynamics of extrasolar planetary systems can be quite different from that of our solar system. More than 200 extrasolar planets have now been found, including at least 20 systems with multiple planets, some in resonant configurations. Their diversity must originate in the properties of the protoplanetary disc of dusty gas out of which they form, the dynamics of the formation of the planetary core, and the subsequent interaction of the planet with the surrounding disc, with other planets, and with the central star. Over the past decade, there has been significant progress on the theoretical aspects of the planet formation process. Two viable models of planet formation have been explored, core accretion (growth of dust into planets through mutual collisions) and gravitational instability in the disc, and several modes of angular momentum exchange between planet and disc have been identified which may explain the proximity of the 51 Peg planet to its star. However, many of the stages of planet formation remain poorly understood. In part this is because of a lack of knowledge of the physical nature of protoplanetary discs, although this has increased dramatically in recent years owing both to observations of the gaseous and dusty components of the discs of pre-main-sequence stars and to computational modelling of their (magneto-) hydrodynamics. The outcome of planet formation is also becoming more tightly constrained, through the growing number of systems known to have either extrasolar planets or planetesimal belts analogous to the asteroid and Kuiper belts. The discovery of planetesimals and dwarf planets in the Kuiper belt beyond Neptune is also leading to a revision in our understanding of the formation and evolution of the outer solar system. The wide array of phenomena seen in all systems is opening up new areas of celestial mechanics. Read more at: http://www.newton.ac.uk/programmes/DDP/