  We present new theoretical estimates of the relative contributions of
unresolved blazars and star-forming galaxies to the extragalactic gamma-ray
background (EGB) and discuss constraints on the contributions from alternative
mechanisms such as dark matter annihilation and truly diffuse gamma-ray
production. We find that the Fermi source count data do not rule out a scenario
in which the EGB is dominated by emission from unresolved blazars, though
unresolved star-forming galaxies may also contribute significantly to the
background, within order-of-magnitude uncertainties. In addition, we find that
the spectrum of the unresolved star-forming galaxy contribution cannot explain
the EGB spectrum found by EGRET at energies between 50 and 200 MeV, whereas the
spectrum of unresolved FSRQs, when accounting for the energy-dependent effects
of source confusion, could be consistent with the combined spectrum of the
low-energy EGRET EGB measurements and the Fermi-LAT EGB measurements.
