The equivalence principle implies that the peculiar motions (deviations from a Hubble flow) of galaxies share the same velocity field as the underlying dark matter velocity field. This is contrast to the biased distribution of galaxies in relation to the density field of the dark matter. The discussion how the peculiar velocities can be used as a probe of the cosmological paradigm, present results inferred from the large scale motions of galaxies and discuss challenges and way to overcome them.