Invited review abstract

We review recent work on the role of magnetic fields in the
cloud to core transition as well as the transition of a core to a star-disk system.
On the cloud scale, large scale nonlinear flows can create compressed cloud
layers. If the cloud has a subcritical mass-to-flux ratio,
ambipolar diffusion occurs rapidly in the compressed layers.
The qualitative result is a handful of cores
that are formed within elongated ridges, while the bulk of the cloud does
not form stars. In the flux-freezing limit
that may be applicable to photoionized molecular cloud envelopes, supersonic
motions can persist for very long times if the cloud is subcritical.
In the case of protostellar accretion, rapid magnetic diffusion (through
ohmic dissipation with additional support from ambipolar diffusion) near the protostar
causes dramatic magnetic flux loss. By doing so, it also allows the formation of
a centrifugal disk, thereby avoiding the magnetic braking catastrophe.