The High-z Emission Line Survey (HiZELS) is targeting H alpha emitters at z similar to 0.8 - 2.2, and, by probing large volumes down to faint fluxes with WFCAM on UKIRT, is resulting in the largest samples of high-z H alpha selected star-forming galaxies. With HiZELS, we have accurately measured the evolution of the H alpha luminosity function up to z > 2 in a fully consistent way and determined the H alpha-based star formation history of the Universe since z similar to 2.2 for the first time. We have found important morphology-H alpha relations and have been able to show that it is the evolution of disk galaxies from z similar to 1 to z similar to 0 that is responsible for the decline in the cosmic star formation activity not the decline in merger activity. Furthermore, we have conducted the first detailed clustering analysis of H alpha emitters at z similar to 1 and their evolution up to z > 2, not only finding strong relations with H alpha luminosity and infra-red luminosity, but also suggesting a single, fundamental relation valid over the last 10 Gyrs, relating the dark-matter halo mass and quenching of star-formation across cosmic time. HiZELS is probing a large variety of environments, enabling us to detail the dependence of star formation activity on environment and stellar mass, reconciling previous contradictory results in the literature and providing a much sharper view of our understanding at z similar to 1.