  We present numerical simulations and explore scalings and anisotropy of
compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas
pressure dominated (high beta) and magnetically dominated (low beta) plasmas at
different Mach numbers. In addition, we present results for superAlfvenic
turbulence and discuss in what way it is similar to the subAlfvenic turbulence.
We describe a technique of separating different magnetohydrodynamic (MHD) modes
(slow, fast and Alfven) and apply it to our simulations. We show that, for both
high and low beta cases, Alfven and slow modes reveal the Kolmogorov spectrum
(index=-5/3) and scale-dependent Goldreich-Sridhar anisotropy, while fast modes
exhibit spectrum with index=-3/2 and isotropy. We discuss the statistics of
density fluctuations arising from MHD turbulence at different regimes. Our
findings entail numerous astrophysical implications ranging from cosmic ray
propagation to gamma ray bursts and star formation. In particular, we show that
the rapid decay of turbulence reported by earlier researchers is not related to
compressibility and mode coupling in MHD turbulence. In addition, we show that
magnetic field enhancements and density enhancements are marginally correlated.
Addressing the density structure of partially ionized interstellar gas on AU
scales, we show that the new regime of MHD turbulence that we earlier reported
for incompressible flows persists for compressible turbulence and therefore may
provide an explanation for those mysterious structures.
