  We estimate the contribution of AGNs and of their host galaxies to the
infrared background. We use the luminosity function and evolution of AGNs
recently determined by the hard X-ray surveys, and new Spectral Energy
Distributions connecting the X-ray and the infrared emission, divided in
intervals of absorption. These two ingredients allow us to determine the
contribution of AGNs to the infrared background by using mostly observed
quantities, with only minor assumptions. We obtain that AGN emission
contributes little to the infrared background ($<$5% over most of the infrared
bands), implying that the latter is dominated by star formation. However, AGN
host galaxies may contribute significantly to the infrared background, and more
specifically 10--20% in the 1--20$\mu$m range and $\sim$5% at $\lambda<60\mu
m$. We also give the contribution of AGNs and of their host galaxies to the
source number counts in various infrared bands, focusing on those which will be
observed with Spitzer. We also report a significant discrepancy between the
expected contribution of AGN hosts to the submm background and bright submm
number counts with the observational constraints. We discuss the causes and
implications of this discrepancy and the possible effects on the Spitzer far-IR
bands.

Astrophysics