  We present the results of calculations of the cosmic AGN background spectrum
from 3 keV (4\times 10^{-4} microns) to 1000 microns. These computations make
use of the measured X-ray luminosity function and its evolution, as well as
fits from synthesis models of the cosmic X-ray background (CXB) to predict the
AGN contribution to the cosmic infrared background (CIRB) for different models
of the location and distribution of the absorbing material. By comparing our
results to observational constraints we conclude that the current deep Spitzer
surveys can account for the entire AGN contribution to the CIRB at 24 microns,
but these AGN are almost all Compton-thin. In fact, the calculations show that
Compton-thick AGN are a small fraction of the CIRB for \lambda < 100 microns.
For this reason, the most efficient method of identifying the Compton-thick AGN
population is through hard X-ray imaging at energies >~ 40 keV. Selection of
AGN based on their rest-frame near-IR colors will miss low luminosity type 2
AGN due to contamination from the host galaxy. Finally, the AGN that dominate
the CXB must have star formation rates < 100 M_{sun} yr^{-1}, consistent with
them having similar properties as the sources which dominate the CIRB at z ~1.
Including the estimated re-radiated emission from star formation, AGN and their
host galaxies may contribute ~30% of the CIRB at 70 microns, dropping to ~10%
at 24 microns and ~1% at 1-10 microns.
