Studying exoplanets with their parent stars is crucial to understand their population, formation and history. We review some of the key questions regarding their evolution with particular emphasis on giant gaseous exoplanets orbiting close to solar-type stars. For masses above that of Saturn, transiting exoplanets have large radii indicative of the presence of a massive hydrogen-helium envelope. Theoretical models show that this envelope progressively cools and contracts with a rate of energy loss inversely proportional to the planetary age. The combined measurement of planetary mass, radius and a constraint on the (stellar) age enables a global determination of the amount of heavy elements present in the planet interior. The comparison with stellar metallicity shows a correlation between the two, indicating that accretion played a crucial role in the formation of planets. The dynamical evolution of exoplanets also depends on the properties of the central star. We show that the lack of massive giant planets and brown dwarfs in close orbit around G-dwarfs and their presence around F-dwarfs are probably tied to the different properties of dissipation in the stellar interiors. Both the evolution and the composition of stars and planets are intimately linked.