  This article reviews the concept of Lorentz invariant relative velocity that
is often misunderstood or unknown in high energy physics literature. The
properties of the relative velocity allow to formulate the invariant flux and
cross section without recurring to non--physical velocities or any assumption
about the reference frame. Applications such as the luminosity of a collider,
the use as kinematic variable, and the statistical theory of collisions in a
relativistic classical gas are reviewed. It is emphasized how the hyperbolic
properties of the velocity space explain the peculiarities of relativistic
scattering.
