  We discuss HD and MHD compressible turbulence as a cloud-forming and
cloud-structuring mechanism in the ISM. Results from a numerical model of the
turbulent ISM at large scales suggest that the phase-like appearance of the
medium, the typical values of the densities and magnetic field strengths in the
intercloud medium, as well as the velocity dispersion-size scaling relation in
clouds may be understood as consequences of the interstellar turbulence.
However, the density-size relation appears to only hold for the densest clouds,
suggesting that low-column density clouds, which are hardest to observe, are
turbulent transients. We then explore some properties of highly compressible
polytropic turbulence, in one and several dimensions, applicable to molecular
cloud scales. At low values of the polytropic index $\gamma$, turbulence may
induce the gravitational collapse of otherwise linearly stable clouds, except
if they are magnetically subcritical. The nature of the density fluctuations in
the high Mach-number limit depends on $\gamma$, and in no case resembles that
resulting from Burgers turbulence. In the isothermal ($\gamma=1$) case, the
dispersion of $\ln (\rho)$ scales like the turbulent Mach number. The latter
case is singular with a lognormal density pdf, while power-law tails develop at
high (resp. low) densities for $\gamma <1$ (resp. $\gamma >1$).
