Galaxy redshift and peculiar velocity surveys provide a wealth of insight on cosmology, dark matter, and dark energy. Peculiar velocities can be measured at z=0 with hundreds of luminosity distances, or inferred at z>0 with Redshift Space Distortions (RSDs) from thousands of redshifts. In this talk, I'll present results with both methods which can appear in tension with Lambda-CDM. Many recent RSD measurements are systematically lower than LCDM, hinting that w>-1 (although with a surprisingly low scatter in the data). At z=0, the velocity dipole is several times higher than LCDM. I'll show results from the COMPOSITE peculiar velocity catalogue - the largest to date - and show that the tension with LCDM is dramatically reduced with higher-order moments of the velocity field, and present new, unbiased measurements of the matter power spectrum. I'll then present forecast results for future velocity and redshift surveys, in particular WEAVE - a new, extremely large redshift survey on the William Herschel Telescope - and compare the results to a survey similar to the Euclid spectroscopic survey. I'll show that both surveys will measure powerful and complementary results for dark energy, and forecast measurements for the properties of neutrinos, axions, and modified gravity.