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The Magellanic Clouds are two of the closest galaxies to the Milky Way, with the Large Magellanic Cloud (LMC) at a distance of ~ 50 kpc and the Small Magellanic Cloud (SMC) at ~ 62 kpc. Because of their proximity, they are two of the best-studied galaxies in the Universe. As such, they are a benchmark for studies on various topics, including stellar populations and the interstellar medium, microlensing by dark objects, and the cosmological distance scale. As nearby companions of the Milky Way with significant signs of mutual interaction, they have also been taken as examples of hierarchical structure formation in the Universe. For all these applications it is important to have an understanding of the kinematics of the LMC and the SMC, as well the kinematics (i.e., orbit) of their center of mass with respect to the Milky Way and with respect to each other. These topics form the subject of the present review. Other related topics, such as the more general aspects of the structure of the LMC and SMC, the nature of the LMC bar, the possible presence of fore- or background populations, and the large radii extent of the Clouds are not discussed here. The nature, origin, and models of the Magellanic Stream are touched upon only briefly. All these topics are reviewed in others papers in this volume by, e.g., Harris, Majewski, Besla, Bekki, and others.