  We review theoretical models of the early stages of star formation, in which
gravitational collapse is strongly regulated by magnetic fields and the
associated process of ambipolar diffusion. We discuss results of numerical
simulations and analytical studies of core formation and collapse, which can be
directly tested against observation. We also focus on recent data which are
relevant to this theory of star formation, such as: observations of extended
infall in protostellar cores, estimates of evolutionary timescales ~ 1 Myr for
cores, measured mass-to-flux ratios of cores, and the relative alignment of
polarization vectors with apparent cloud elongation. It is shown that in all of
these areas, the data lie within the observationally allowable range of
parameter space. Other areas of interest (protostellar accretion rates and the
presence of core edges) and issues that remain unresolved or under study (the
role of non-thermal motions and cluster formation) are also discussed.
Moreover, we highlight some differences between our model predictions and those
of highly turbulent star formation models, and discuss how these differences
can be distinguished observationally.
