  We review the role that magnetic field may have on the formation and
evolution of molecular clouds. After a brief presentation and main assumptions
leading to ideal MHD equations, their most important correction, namely the
ion-neutral drift is described. The nature of the multi-phase interstellar
medium (ISM) and the thermal processes that allows this gas to become denser
are presented. Then we discuss our current knowledge of compressible magnetized
turbulence, thought to play a fundamental role in the ISM. We also describe
what is known regarding the correlation between the magnetic and the density
fields. Then the influence that magnetic field may have on the interstellar
filaments and the molecular clouds is discussed, notably the role it may have
on the prestellar dense cores as well as regarding the formation of stellar
clusters. Finally we briefly review its possible effects on the formation of
molecular clouds themselves. We argue that given the magnetic intensities that
have been measured, it is likely that magnetic field is i) responsible of
reducing the star formation rate in dense molecular cloud gas by a factor of a
few, ii) strongly shaping the interstellar gas by generating a lot of filaments
and reducing the numbers of clumps, cores and stars, although its exact
influence remains to be better understood. % by a factor on the order of at
least 2. Moreover at small scales, magnetic braking is likely a dominant
process that strongly modifies the outcome of the star formation process.
Finally, we stress that by inducing the formation of more massive stars,
magnetic field could possibly enhance the impact of stellar feedback.
