Abstract: In this review we consider the main rotation regimes that are inherent for planetary satellites of the Solar System, satellites of trans-Neptunian objects, and potential satellites of extrasolar planets. Both the findings of classical theoretical studies and the recent conclusions on the observed rotational dynamics of satellites and their long-term dynamical tidal evolution are described. We concentrate on a regime of a satellite’s rotation that is synchronous with its orbital motion and is observed for all major planetary satellites (radius of the figure larger than ~500 km). We also consider irregularly shaped minor satellites (with a figure radius less than ~300 km), rotating regularly and much faster than in the case of synchronous rotation. The regime of chaotic rotation (tumbling) observed for the seventh satellite of Saturn, Hyperion, is analyzed at length. We also discuss the possibility of chaotic rotation of other minor satellites. Results and research prospects for the rotational dynamics of exomoons are presented.