  Particle acceleration by magnetic reconnection is now recognized as an
important process in magnetically dominated regions of galactic and
extragalactic black hole sources. This process helps to solve current puzzles
specially related to the origin of the very high energy flare emission in these
sources. In this review, we discuss this acceleration mechanism and show recent
analytical studies and multidimensional numerical SRMHD and GRMHD (special and
general relativistic magnetohydrodynamical) simulations with the injection of
test particles, which help us to understand this process both in relativistic
jets and coronal regions of these sources. The very high energy and neutrino
emission resulting from the accelerated particles by reconnection is also
discussed.
