  We construct rest-frame luminosity functions at 3.6, 4.5, 5.8, 8 and 24
microns over the redshift range 0<z<2 for galaxies and 0<z<4 for optical QSOs,
using optical and infrared data from the Spitzer Wide-area InfraRed
Extragalactic survey. The 3.6 and 4.5 micron galaxy LFs show evidence for
moderate positive luminosity evolution up to z~1.5, consistent with the passive
ageing of evolved stellar populations. Their comoving luminosity density was
found to evolve passively, gradually increasing out to z~0.5-1 but flattening,
or even declining, at higher redshift. Conversely, the 24 micron galaxy LF,
which is more sensitive to obscured star formation and/or AGN activity,
undergoes strong positive evolution, with the derived IR energy density and SFR
density proportional to (1+z)^gamma with gamma=4.5^{+0.7}_{-0.6} and the
majority of this evolution occurring since z~1. Optical QSOs, however, show
positive luminosity evolution in all bands, out to the highest redshifts
(3<z<4). Modelling as L* proportional to (1+z)^gamma gave
gamma=1.3^{+0.1}_{-0.1} at 3.6 micron, gamma=1.0^{+0.1}_{-0.1} at 4.5 micron
and stronger evolution at the longer wavelengths (5.8, 8 and 24 micron), of
gamma~3. Comparison of the galaxy LFs to predictions from a semi-analytic model
based on CDM indicate that an IMF skewed towards higher mass star formation in
bursts compared to locally is preferred. As a result the currently inferred
massive star formation rates in distant sub-mm sources may require substantial
downwards revision.
