Particle acceleration by magnetic reconnection is currently regarded as an important process in magnetically dominated regions of galactic and extragalactic sources like the surrounds of black holes and in relativistic jets. This process may help to solve current puzzles specially related to the interpretation of the very high energy emission produced by these sources.
In this lecture, I will discuss this acceleration process briefly, especially when reconnection is driven by turbulence. Then I will discuss this process in the framework of the sources above, showing recent analytical and multidimensional numerical MHD studies that indicate that fast reconnection can be a powerful process to accelerate particles to relativistic velocities, produce the associated high energy non-thermal emission, and account for efficient conversion of magnetic into kinetic energy in these flows.