  (Abridged) We present new theoretical predictions for surface brightness
fluctuations (SBFs) using models optimized for this purpose. Our predictions
agree well with SBF data for globular clusters and elliptical galaxies. We
provide refined theoretical calibrations and k-corrections needed to use SBFs
as standard candles. We suggest that SBF distance measurements can be improved
by using a filter around 1 micron and calibrating I-band SBFs with the
integrated V-K galaxy color. We also show that current SBF data provide useful
constraints on population synthesis models, and we suggest SBF-based tests for
future models. The data favor specific choices of evolutionary tracks and
spectra in the models among the several choices allowed by comparisons based on
only integrated light. In addition, the tightness of the empirical I-band SBF
calibration suggests that model uncertainties in post-main sequence lifetimes
are less than +/-50% and that the IMF in ellipticals is not much steeper than
that in the solar neighborhood. Finally, we analyze the potential of SBFs for
probing unresolved stellar populations. We find that optical/near-IR SBFs are
much more sensitive to metallicity than to age. Therefore, SBF magnitudes and
colors are a valuable tool to break the age/metallicity degeneracy. Our initial
results suggest that the most luminous stellar populations of bright cluster
galaxies have roughly solar metallicities and about a factor of three spread in
age.
