Accretion provides the energy for the most spectacular phenomena observed in astronomy: gamma-ray bursts, quasars, and emergence of gravitational waves. In my lecture I will concentrate mostly on semi-stationary accretion processes behind the persistent sources of emission. I will present the basic theoretical background needed to understand the accretion process, and the theory will be used to confront with the data in order to see which aspects of the accretion process in different objects is understood, and where the progress in being slow.