We discuss
 turbulence in the interstellar medium, specifically
in cool molecular clouds and star-forming regions. Local
overdensities (clouds) in these regions are known to be
supersonically turbulent, with typical Mach numbers on
the order of ten or more. We develop a model for turbulence in these clouds in
which individual clouds dissipate their turbulent kinetic
energy internally, and this internal dissipation is
balanced in the mean by the injection of kinetic energy
from strong shocks that arrive intermittently. Physically,
these shocks correspond to the shocks from supernovae
as well as other explosive events. We find that such a model nicely
predicts the existence of large internal velocities
with non-Gaussian statistics, as well as the observed
phenomenological relationship between cloud size
and line width. We also discuss star formation within
the context of this model.