Black holes provide a crucial link between Einstein’s theory of gravity and real cosmic objects which astronomers can observe and study in the Universe. This project is oriented towards legacy of the cornerstone XMM-Newton X-ray satellite mission of European Space Agency (ESA) in synergy with relevant data in other spectral domains that are covered by ground-based infrared and radio interferometric techniques at European Southern Observatory (ESO) and elsewhere. Information in different wavelengths will be gathered and explored in order to understand radiation processes in places of strong gravity, near black holes. We will address outstanding questions of determining the black hole spin, measuring the location of the accretion disc inner rim, and revealing connections between inflows and outflows in these objects. To this end we will analyze and interpret multi-wavelength spectral and fast timing information on accreting black holes in compact binaries, in cores of active galactic nuclei, as well as other galaxies exhibiting low level of activity due to intermittent supply of gas from the cosmic environment or by switching to a radiatively inefficient regime. We will include valuable data from archives and complement them by performing new observations where needed. Our main objective is to use and enhance computational tools that the participating groups have been developing over two decades, and to join our effort in a dedicated program of data analysis and science interpretation of the most bizarre cosmic objects. We will rely on unprecedented combination of sensitivity and energy resolution of current X-ray missions of ESA, together with wide spectral coverage by ground-based observatories in ESO and elsewhere. The developed techniques will be highly relevant in the context of new missions. We will make our tools available to the entire scientific community. The research team includes experts from 7 leading research institutes and universities.