  Turbulence 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.
