  Growing supermassive black holes (Active Galactic Nuclei; AGN) release energy
with the potential to alter their host galaxies and larger-scale environment; a
process named "AGN feedback". Feedback is a required component of galaxy
formation models and simulations to explain observed properties of galaxy
populations. We provide a broad overview of observational approaches that are
designed to establish the physical processes that couple AGN energy to the
multi-phase gas, or to find evidence that AGN impact upon galaxy evolution. The
orders-of-magnitude range in spatial, temporal, and temperature scales,
requires a diverse set of observational studies. For example, studying
individual targets in detail sheds light on coupling mechanisms; however,
evidence for long-term impact of AGN is better established within galaxy
populations that are not necessarily currently active. We emphasise how modern
surveys have revealed the importance of radio emission for identifying, and
characterising, feedback mechanisms. At the achieved sensitivities, the
detected radio emission can trace a range of processes, including shocked
interstellar medium caused by AGN outflows (driven by various mechanisms
including radiation pressure, accretion disc winds, and jets). We also describe
how interpreting observations in the context of theoretical work can be
challenging, in part, due to some of the adopted terminology.
