Galaxies are not only beautiful and diverse—they are luminous and abundant engines of cosmic evolution, forming within vast reservoirs of gas and often anchored by a central, supermassive black hole. Far from being quiet, these SMBHs transform their host galaxies. As they accrete material, they can release extraordinary bursts of energy and momentum that regulate the flow of gas into the galaxy and alter the course of its star formation. Nevertheless, the precise physical mechanisms by which SMBH feedback influences galaxy formation are not yet fully understood. In particular, their role in diverse cosmic environments and epochs still has some open questions, especially with the advent of state-of-the-art telescope surveys.