  We review past work using broad emission lines as virial estimators of black
hole masses in quasars. Basically one requires estimates of the emitting region
radius and virial velocity dispersion to obtain black hole masses. The three
major ways to estimate the broad-line emitting region (BLR) radius involve: (1)
direct reverberation mapping, (2) derivation of BLR radius for larger samples
using the radius-luminosity correlation derived from reverberation measures,
and (3) estimates of BLR radius using the definition of the ionization
parameter solved for BLR radius (photoionization method). At low redshift (z <
0.7) FWHM H-beta serves as the most widely used estimator of virial velocity
dispersion. FWHM H-beta can provide estimates for tens of thousands of quasars
out to z ~ 3.8 (IR spectroscopy beyond z ~ 1). A new photoionization method
also shows promise for providing many reasonable estimates of BLR radius via
high S/N IR spectroscopy of the UV region 1300 -- 2000 A. FWHM MgII 2800 can
serve as a surrogate for FWHM H-beta in the range 0.4 < z < 6.5 while CIV 1549
is affected by broadening due to non-virial motions and best avoided (i.e.
there is no clear conversion factor between FWHM H-beta and FWHM CIV 1549).
Most quasars yield black hole mass estimates in the range 7 < log M< 9.7. There
is no strong evidence for values above 10.0 and there may be evidence for a
turnover in the maximum black hole mass near z ~ 5.
