The detection and characterization of extrasolar planets clearly appears as one of the main goals of observational astronomy for the coming years. Space and ground project are numerous, but theoretical studies aimed at analyzing and understanding available and future data are needed. During this thesis, I study various physical processes affecting the internal structure and evolution of both solar, and extrasolar giant planets. In particular I investigate: - The impact of the intense stellar irradiation received by a close in planet on its subsequent internal evolution. This allows me to quantify the radius anomaly of bloated Hot Jupiters and to constrain their internal composition. - The tidal and centrifugal distortion of a fluid planet. By using both analytical and numerical models, I show how non-sphericity of the planet affects transit measurements, yielding an underestimation of its radius. - How the presence of double-diffusive convection caused by a heavy elements gradient in the gaseous envelope of a planet can decrease the efficiency of its internal heat transport, and affect its structure and evolution. - The coupling between the orbital and the thermal evolution of a planet arising from the strong star-planet tidal interaction. Subsequently, I find that tidal heating alone is not a viable explanation for the observed radius anomaly of transiting planets. Through these different studies, I developed various analytical models and numerical codes that are both flexible and robust, and which now allow one to study the properties of new extrasolar planets and brown dwarfs as they are discovered.