Measuring galaxy peculiar velocities provides powerful new tests of the theory of gravity on cosmological scales, that are complementary to other cosmic probes. We present new cosmological fits to the most powerful existing dataset, the 6-degree Field Galaxy Survey velocity sample, which (in disagreement with some previous velocity data) are in concordance with the standard cosmological model. We explain our improvements in data analysis and modelling of velocity power spectrum. Looking forward, we also present new forecasts for how future velocity surveys performed with the Australian Square Kilometre Array Pathfinder will produce competitive tests of cosmology.