  Astrophysical turbulence is magnetohydrodynamic (MHD) in its nature. We
discuss fundamental properties of MHD turbulence. In particular, we discuss the
generation of compressible MHD waves by Alfvenic turbulence and show that this
process is inefficient. This allows us to study the evolution of different
types of MHD perturbations separately.
  We describe how to separate MHD fluctuations into 3 distinct families -
Alfven, slow, and fast modes. We find that the degree of suppression of slow
and fast modes production by Alfvenic turbulence depends on the strength of the
mean field. We show that Alfven modes in compressible regime exhibit scalings
and anisotropy similar to those in incompressible regime. Slow modes passively
mimic Alfven modes. However, fast modes exhibit isotropy and a scaling similar
to that of acoustic turbulence both in high- and low-beta plasmas. We show that
our findings entail important consequences for theories of star formation,
cosmic ray propagation, dynamics of dust, and gamma ray bursts. We anticipate
many more applications of the new insight to MHD turbulence and expect more
revisions of the existing paradigms of astrophysical processes as the field
matures.
