  The evolution of luminous QSOs is linked to the evolution of massive
galaxies. We know this because the relic black-holes found locally have masses
dependent on the properties of the host galaxy's bulge. An important way to
explore this evolution would be to measure dependences of black hole masses and
Eddington accretion ratios over a range of redshifts, i.e., with cosmological
age. For low redshift QSOs (and their lower luminosity Seyfert galaxy
counterparts) it has been possible to infer black hole masses from the
luminosities and velocity dispersions of their host-galaxy bulges. These masses
agree with those virial black hole masses calculated from the Doppler widths of
the broad Hbeta emission lines. The latter method can then be extended to more
distant and luminous QSOs, up to redshifts of 0.6 with ground-based optical
observations. We discuss ways to extend these explorations to higher redshifts
-- up to about 3 using the widths of QSOs' broad UV emission lines, and in
principle, and to redshifts near 4 from ground-based infrared observations of
rest-frame Hbeta at 2.5 micron. We discuss the possibility of investigating the
accretion history of the higher redshift QSOs using measures of Eddington
accretion ratio -- the soft X-ray spectral index and the eigenvectors of
Principal Components Analyses of QSOs' UV emission-line spectra.
