Magnetic fields in star formation: from clouds to cores
  In this chapter we review recent advances in understanding the roles that
magnetic fields play throughout the star formation process, gained through
observations and simulations of molecular clouds, the dense, star-forming phase
of the magnetised, turbulent interstellar medium (ISM). Recent results broadly
support a picture in which the magnetic fields of molecular clouds transition
from being gravitationally sub-critical and near equipartition with turbulence
in low-density cloud envelopes, to being energetically sub-dominant in dense,
gravitationally unstable star-forming cores. Magnetic fields appear to play an
important role in the formation of cloud substructure by setting preferred
directions for large-scale gas flows in molecular clouds, and can direct the
accretion of material onto star-forming filaments and hubs. Low-mass star
formation may proceed in environments close to magnetic criticality; high-mass
star formation remains less well-understood, but may proceed in more
supercritical environments. The interaction between magnetic fields and
(proto)stellar feedback may be particularly important in setting star formation
efficiency. We also review a range of widely-used techniques for quantifying
the dynamic importance of magnetic fields, concluding that better-calibrated
diagnostics are required in order to use the spectacular range of forthcoming
observations and simulations to quantify our emerging understanding of how
magnetic fields influence the outcome of the star formation process.
