Since 1995 astronomers have discovered and partially characterised several thousand extrasolar planets. Many planets have masses similar to Jupiter's, and orbit their host stars in only a few Earth days -- a fascinating class of planets that we refer to as hot Jupiters. Since these planets orbit their stars very closely, gravitational tidal interactions can determine the orbit and the internal rotations of the planet and its host star. For example, the closest planets, that orbit their stars in less than 10 Earth days, preferentially have circular orbits, while those that orbit their stars more distantly tend to have eccentric orbits. This is thought to be explained by the dissipation of tidal flows inside these planets. These (and related) observations motivate theoretical work to understand tidal flows inside planets and stars, to determine and elucidate the mechanisms by which they may dissipate. This requires understanding the fluid dynamics and magnetohydrodynamics of tidal flows including the effects of rotation, stratification, convection and magnetic fields. This project will investigate some of these effects using a combination of computer simulations and theoretical (analytical) calculations, with the aim to understand tidal flows in stars and in the fluid layers of planets.