Supersonic turbulence is an essential element in understanding how structure within interstellar gas is created and shaped. In the context of star formation, many computational studies show that the mass spectrum of density and velocity fluctuations within dense clouds, as well as the distribution of their angular momenta, trace their origin to the statistical and physical properties of gas that is lashed with shock waves. In this paper, we review the observations, simulations and theories of how turbulent-like processes can account for the structures we see in molecular clouds. We then compare traditional ideas of supersonic turbulence with a simpler physical model involving the effects of multiple shock waves and their interactions in the interstellar medium. Planar intersecting shock waves produce dense filaments and generate vortex sheets that are essential to create the broad range of density and velocity structure in clouds. As an example, the lower-mass behaviour of the stellar initial mass function can be traced to the tendency of a collection of shock waves to build up a lognormal density distribution (or column density). Vorticity—which is essential to produce velocity structure over a very broad range of length scales in shocked clouds—can also be generated by the passage of curved shocks or intersecting planar shocks through such media. Two major additional physical forces affect the structure of star-forming gas—gravity and feedback processes from young stars. Both of these can produce power-law tails at the high-mass end of the initial mass function.