Properties of MHD turbulence and its consequences for the ISM and ICM

It is well known that the interstellar (ISM) and intergalactic (ICM) media are threaded by large scale magnetic fields. The understanding of its role on the dynamics of the media is, however, still in progress. For the ISM, magnetic fields may control or, at least, play a major role on the turbulence cascade leading to the star formation process. The ICM, on the other hand, is assumed to be thermally dominated but still the magnetic field may play an important role on the processes of acceleration and propagation of cosmic rays. In this work we provide a review of the latest theoretical results on the evolution of MHD turbulence under collisional and collisionless plasma approaches.