"Our team has made several advances in our understanding of how young planets interact with their parent protoplanetary discs. We have developed new computer models of systems containing giant planets, which have sufficient mass to open gaps in their parent discs. Although these young planets are mostly invisible to our telescopes their effect on the discs can be observed, and we have shown how new data can be used to understand how young giant planetary systems form and evolve. We have also built sophisticated computer simulations of multi-planet systems, in order to understand how the gravitational interaction between planets can shape the formation and evolution of these systems. In theoretical models pairs of planets often become ""trapped"" in special locations, known as resonances, where the planets' mutual gravity has a strong effect, but very few of these resonances are seen in real systems. Our calculations have shown how the protoplanetary disc can push planets out of resonance, and these calculations will have important implications for our understanding of how observed ""super-Earths"" and Neptune-size planets were formed. We have also studied of planets on inclined discs, and planets and discs in binary systems, using large-scale computer simulations to model the dynamics, evolution, and observational appearance of these systems."