Accuracy levels of metres per second require the fundamental concept of radial velocity for stars and other distant objects to be examined, both as a physical velocity, and as measured by spectroscopic and astrometric techniques. Aiming at definitions that are unambiguous at accuracy levels of 1 m/s, we analyse different concepts of radial velocity and their interrelations. We distinguish between the geometrically defined kinematic radial velocity and astrometric radial velocity on one hand, and the spectroscopically defined barycentric radial-velocity measure on the other. The last two concepts are defined by recent resolutions adopted by the International Astronomical Union (IAU), the motives and consequences of which are explained in this paper.
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