  This chapter describes briefly the key aspects behind the derivation of
precise radial velocities. I start by defining radial velocity precision in the
context of astrophysics in general and exoplanet searches in particular. Next I
discuss the different basic elements that constitute a spectrograph, and how
these elements and overall technical choices impact on the derived radial
velocity precision. Then I go on to discuss the different wavelength
calibration and radial velocity calculation techniques, and how these are
intimately related to the spectrograph's properties. I conclude by presenting
some interesting examples of planets detected through radial velocity, and some
of the new-generation instruments that will push the precision limit further.
