Accuracy levels of metres per second require the concept of ‘radial velocity’ to be examined, in particular with respect to relativistic velocity effects and spectroscopic measurements made inside gravitational fields. Already in a classical (non-relativistic) framework the line-of-sight velocity component is an ambiguous concept. In the relativistic context, the observed wavelength shifts depend e.g. on the transverse velocity of the star and the gravitational potential at the source. We argue that the observational quantity resulting from high-precision radial-velocity measurements is not a physical velocity but a spectroscopic radial-velocity measure, which only for historic and practical reasons is expressed in velocity units. This radial-velocity measure may be defined as cz, where c is the speed of light and z is the observed relative wavelength shift reduced to the solar system barycentre. To first order, cz equals the line-of-sight velocity, but its precise interpretation is model dependent.