  We review the basic techniques for extracting information about quasar
structure and kinematics from the broad emission lines in quasars. We consider
which lines can most effectively serve as virial estimators of black hole mass.
At low redshift the Balmer lines,particularly broad H beta, are the lines of
choice. For redshifts greater than 0.7 - 0.8 one can follow H beta into the IR
windows or find an H beta surrogate. We explain why UV CIV 1549 is not a safe
virial estimator and how MgII 2800 serves as the best virial surrogate for H
beta up to the highest redshift quasar known at z ~ 7. We show how spectral
binning in a parameter space context (4DE1) makes possible a more effective
comparison of H beta and MgII. It also helps to derive more accurate mass
estimates from appropriately binned spectra and, finally, to map the dispersion
in black hole mass and Eddington ratio across the quasar population. FWHM MgII
is about 20% smaller than FWHM H beta in the majority of type 1 AGN requiring
correction when comparing black hole mass estimates from these two lines. The
20% of sources showing narrowest FWHM H beta (< 4000 km/s) and strongest FeII
(R_FeII >~ 1.0) emission (we call them bin A3-4 sources) do not show this FWHM
difference and a blueshift detected in MgII for these sources suggests that
FWHM H beta is the safer virial estimator for these extreme Eddington emitters.
