  We review methods to measure magnetic fields within the corona using the
polarized light in magnetic-dipole (M1) lines. We are particularly interested
in both the global magnetic-field evolution over a solar cycle, and the local
storage of magnetic free energy within coronal plasmas. We address commonly
held skepticisms concerning angular ambiguities and line-of-sight confusion. We
argue that ambiguities are in principle no worse than more familiar remotely
sensed photospheric vector-fields, and that the diagnosis of M1 line data would
benefit from simultaneous observations of EUV lines. Based on calculations and
data from eclipses, we discuss the most promising lines and different
approaches that might be used. We point to the S-like [Fe {\sc XI}] line (J=2
to J=1) at 789.2nm as a prime target line (for ATST for example) to augment the
hotter 1074.7 and 1079.8 nm Si-like lines of [Fe {\sc XIII}] currently observed
by the Coronal Multi-channel Polarimeter (CoMP). Significant breakthroughs will
be made possible with the new generation of coronagraphs, in three distinct
ways: (i) through single point inversions (which encompasses also the analysis
of MHD wave modes), (ii) using direct comparisons of synthetic MHD or
force-free models with polarization data, and (iii) using tomographic
techniques.
