Using multi-wavelength surveys, we measure the growth of supermassive black holes at the centres of galaxies over the last 12 billion years. Most actively growing black holes are heavily obscured and not seen in large optical surveys; at the same time, the deep multi-wavelength surveys too little of the sky to find rare objects like luminous quasars. So completing the census of black hole growth requires a large-volume X-ray survey, to explore hidden, high luminosity and distant black holes. Theorists have suggested that mergers of gas-rich galaxies trigger Active Galactic Nuclei (AGN), whose radiation and outflows may quench star formation and strongly affect galaxy evolution. Our morphological analyses show that mergers probably do trigger luminous quasars but not the far more numerous moderate-luminosity AGN, which grow slowly through secular processes.