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 γ, 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 γ. In the isothermal (γ = 1) case, the dispersion of In (ρ) 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 γ < 1 (resp. γ > 1). As a consequence, density fluctuations originating from Burgers turbulence are similar to those of the polytropic case only at high density when γ « 1 and M » 1.