Astrophysical black holes in nuclei of galaxies are of indisputable relevance to the current research. These extreme objects are of immense interest to pure relativists as well as observational astronomers. We will present an overview of selected aspects of physical processes occurring in the inner regions of Active Galactic Nuclei (AGN). Observational evidence strongly suggests that strong gravitational fields play a significant role in governing the energy output of AGN and their influence on the surrounding medium. In order to reduce an unnecessary overlap with numerous reviews and textbooks on the similar subject, we focus on just a few topics, such as the launching scenarios of nuclear outflows and jets that start and pre-collimate in the immediate vicinity of black holes. We will discuss the interaction between magnetic and gravitational fields in the strong-gravity regime of General Relativity.