  We review recent results from numerical simulations and related models of MHD
turbulence in the interstellar medium (ISM) and in molecular clouds. We discuss
the implications of turbulence for the processes of cloud formation and
evolution, and the determination of clouds' physical properties. Numerical
simulations of the turbulent ISM to date have included magnetic fields,
self-gravity, parameterized heating and cooling, modeled star formation and
other turbulent inputs. The structures which form reproduce well observed
velocity-size scaling properties, while predicting the non-existence of a
general density-size scaling law. Criteria for the formation of
gravitationally-bound structures by turbulent compression are summarized. For
flows with equations of state $P\propto \rho^\gamma$, the statistics of the
density field depend on the exponent $\gamma$. Numerical simulations of both
forced and decaying MHD compressible turbulence have shown that the decay rate
is comparable to the non-magnetic case. For virialized clouds, the turbulent
decay time is shorter than the gravitational free-fall time, so wholesale cloud
collapse is only prevented by ongoing turbulent inputs and/or a strong mean
magnetic field. Finally, perspectives for future work in this field are briefly
discussed.
