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Hundreds of planets are already known to have orbits only a few times wider than the stars that host them. The tidal interaction between a planet and its host star is one of the main agents shaping the observed distributions of properties of these systems. Tidal dissipation in the planet tends make the orbit circular, as well as synchronizing and aligning the planet’s spin with the orbit, and can significantly heat the planet, potentially affecting its size and structure. Dissipation in the star typically leads to inward orbital migration of the planet, accelerating the star’s rotation, and in some cases destroying the planet. Some essential features of tidal evolution can be understood from the basic principles that angular momentum and energy are exchanged between spin and orbit by means of a gravitational field and that energy is dissipated. For example, most short-period exoplanetary systems have too little angular momentum to reach a tidal equilibrium state. Theoretical studies aim to explain tidal dissipation quantitatively by solving the equations of fluid and solid mechanics in stars and planets undergoing periodic tidal forcing. The equilibrium tide is a nearly hydrostatic bulge that is carried around the body by a large-scale flow, which can be damped by convection or hydrodynamic instability, or by viscoelastic dissipation in solid regions of planets. The dynamical tide is an additional component that generally takes the form of internal waves restored by Coriolis and buoyancy forces in a rotating and stratified fluid body. It can lead to significant dissipation if the waves are amplified by resonance, are efficiently damped when they attain a very short wavelength, or break because they exceed a critical amplitude. Thermal tides are excited in a planetary atmosphere by the variable heating by the star’s radiation. They can oppose gravitational tides and prevent tidal locking, with consequences for the climate and habitability of the planet. Ongoing observations of transiting exoplanets provide information on the orbital periods and eccentricities as well as the obliquity (spin–orbit misalignment) of the star and the size of the planet. These data reveal several tidal processes at work and provide constraints on the efficiency of tidal dissipation in a variety of stars and planets.