Tracing AGN feedback, from the SMBH horizon up to cluster scales

Observations performed in the last decades have shown that supermassive black holes (SMBHs) and cosmic structures are not separate elements of the Universe. While galaxies extend on spatial scales about ten orders of magnitude larger than the horizon of SMBHs, black holes would not exist without matter feeding them, and cosmic structures would not be the same without feedback from SMBHs. Powerful winds/jets in active galactic nuclei (AGN) may be the basis of this co-evolution. Synergistic observations in the X-rays and other wavebands have been proven to be fundamental to map AGN winds from the event horizon up to galaxy scales, providing a promising avenue to study the multi-phase SMBH feeding and feedback processes. Moreover, a spatially resolved, spectroscopic analysis of AGN in clusters will allow us to probe the multiphase medium ranging from galactic up to cluster scales. Revolutionary advances are expected in the upcoming decade with new multi-wavelength observatories, ranging from radio to X-rays.