Compact objects, the ultimate stage of evolution of massive stars, are strong X- and gamma-ray emitters. The compact object (white dwarf, neutron star, or black hole) accretes matter and electromagnetic fields from the close environment. During this process, a part of the gravitational potential energy is reprocessed into kinetic energy in the magnetised fluid. The interplay of turbulence and/or shock generation allows a fraction of this energy to be transfered to a tiny supra-thermal particle population and ultimately to be radiated away into high energy photons. The radiation can be produced in a limited number of ways: cyclo-synchrotron and bremsstrahlung processes; the Compton effect; nuclear interactions and pair creation/absorption. This lecture presents the main properties of the aforementioned mechanisms and illustrates them in some astrophysical situations.