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.

Most of the X-ray emission from luminous accreting black holes emerges from within 20 gravitational radii. The effective emission radius is several times smaller if the black hole is rapidly spinning. General Relativistic effects can then be very important. Large spacetime curvature causes strong lightbending and large gravitational redshifts. The hard X-ray, power-law-emitting corona irradiates the accretion disc generating an X-ray reflection component. Atomic features in the reflection spectrum allow gravitational redshifts to be measured. Time delays between observed variations in the power-law and the reflection spectrum (reverberation) enable the physical scale of the reflecting region to be determined. The relative strength of the reflection and power-law continuum depends on light bending. All of these observed effects enable the immediate environment of the black hole where the effects of General Relativity are on display to be probed and explored.

In strong magnetic fields of neutron stars electron-positron vacuum behaves as an anisotropic medium. Vacuum influences the generation and propagation of electromagnetic radiation in plasma and changes the spectrum of radiation. As a result the change of cyclotron lines shape and appearance of specific “vacuum lines” should be observed in X-ray spectra of accreting neutron stars.