  The peculiar motion of galaxies can be a particularly sensitive probe of
gravitational collapse. As such, it can be used to measure the dynamics of dark
matter and dark energy as well the nature of the gravitational laws at play on
cosmological scales. Peculiar motions manifest themselves as an overall
anisotropy in the measured clustering signal as a function of the angle to the
line-of-sight, known as redshift-space distortion (RSD). Limiting factors in
this measurement include our ability to model non-linear galaxy motions on
small scales and the complexities of galaxy bias. The anisotropy in the
measured clustering pattern in redshift-space is also driven by the unknown
distance factors at the redshift in question, the Alcock-Paczynski distortion.
This weakens growth rate measurements, but permits an extra geometric probe of
the Hubble expansion rate. In this chapter we will briefly describe the
scientific background to the RSD technique, and forecast the potential of the
SKA phase 1 and the SKA2 to measure the growth rate using both galaxy
catalogues and intensity mapping, assessing their competitiveness with current
and future optical galaxy surveys.
