2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/5271Turbulence is the most common state of astrophysical flows. In typical astrophysical fluids, turbulence is accompanied by strong magnetic fields, which has a large impact on the dynamics of the turbulent cascade. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD) turbulence. For the first time we have a scaling model that is supported by both observations and numerical simulations. We review recent progress in studies of both incompressible and compressible turbulence. We compare Iroshnikov-Kraichnan and Goldreich-Sridhar models, and discuss scalings of Alfven, slow, and fast waves. We discuss the implications of this new insight into MHD turbulence for cosmic ray transport.27 pages, 7 figures, invited review, to be published in "Recent Reaserch Developments in Astrophyics" (Research Signpost)(slightly modified)AstrophysicsFluid DynamicsPlasma Physicstext