  Linearly polarized emission from dust grains and molecular spectroscopy is an
effective probe of the magnetic field topology in the interstellar medium and
molecular clouds. The longstanding Davis-Chandrasekhar-Fermi (DCF) method and
the recently developed Histogram of Relative Orientations (HRO) analysis and
the polarization-intensity gradient (KTH) method are widely used to assess the
dynamic role of magnetic fields in star formation based on the plane-of-sky
component of field orientations inferred from the observations. We review the
advances and limitations of these methods and summarize their applications to
observations. Numerical tests of the DCF method, including its various
variants, indicate that its largest uncertainty may come from the assumption of
energy equipartition, which should be further calibrated with simulations and
observations. We suggest that the ordered and turbulent magnetic fields of
particular observations are local properties of the considered region. An
analysis of the polarization observations using DCF estimations suggests that
magnetically trans-to-super-critical and averagely trans-to-super-Alfv\'{e}nic
clumps/cores form in sub-critical clouds. High-mass star-forming regions may be
more gravity-dominant than their low-mass counterparts due to higher column
density. The observational HRO studies clearly reveal that the preferential
relative orientation between the magnetic field and density structures changes
from parallel to perpendicular with increasing column densities, which, in
conjunction with simulations, suggests that star formation is ongoing in
trans-to-sub-Alfv\'{e}nic clouds. There is a possible transition back from
perpendicular to random alignment at higher column densities. Results from
observational studies using the KTH method broadly agree with those of the HRO
and DCF studies.
