The process by which matter accumulates onto a compact object under the influence of gravity. During star formation, gas is accreted onto thecoreof the stars as its total mass is built up and the central temperature increases. Accretion of the matter onto compact stars such as white dwarfs, neutron stars and black holes results in a large release of energy. Accretion of matter onto supermassive black holes in active galactic nuclei is the likely source of their enormous luminosities.