  Compressible turbulence, especially the magnetized version of it, traditionally has a bad reputation with researchers. However, recent progress in theoretical understanding of incompressible MHD as well as that in computational capabilities enabled researchers to obtain scaling relations for compressible MHD turbulence. We discuss scalings of Alfven, fast, and slow modes in both magnetically dominated (low $\beta$) and gas pressure dominated (high $\beta$) plasmas. We also show that the new regime of MHD turbulence below viscous cutoff reported earlier for incompressible flows persists for compressible turbulence. Our recent results show that this leads to density fluctuations. New understanding of MHD turbulence is likely to influence many key astrophysical problems. 
Compressible MHD Turbulence: Mode Coupling, Anisotropies and Scalings