  The peculiar velocities of galaxies are driven by gravity, and hence hold the
promise of probing details of how gravity forms structures. In particular it is
possible to constrain cosmological parameters and to test extensions to the
standard model, such as modifications to the theory of gravity or the existence
of primordial density perturbations which are non-Gaussian. This constraining
power has been frustrated by systematic effects, but we appear to be entering
an era when velocity measurements may finally be living up to their promise.
