  We examine the Velocity Distribution Function (VDF) in dark matter halos from
Milky Way to cluster mass scales. We identify an empirical model for the VDF
with a wider peak and a steeper tail than a Maxwell--Boltzmann distribution,
and discuss physical explanations. We quantify sources of scatter in the VDF of
cosmological halos and their implication for direct detection of dark matter.
Given modern simulations and observations, we find that the most significant
uncertainty in the VDF of the Milky Way arises from the unknown radial position
of the solar system relative to the dark matter halo scale radius.
