  Recent progress in astrophysical hydromagnetic turbulence is being reviewed.
The physical ideas behind the now widely accepted Goldreich--Sridhar model and
its extension to compressible magnetohydrodynamic turbulence are introduced.
Implications for cosmic ray diffusion and acceleration is being discussed.
Dynamo-generated magnetic fields with and without helicity are contrasted
against each other. Certain turbulent transport processes are being modified
and often suppressed by anisotropy and inhomogeneities of the turbulence, while
others are being produced by such properties, which can lead to new large-scale
instabilities of the turbulent medium. Applications of various such processes
to astrophysical systems are being considered.
