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.