  We present new measurements of the evolution of the X-ray luminosity
functions (XLFs) of unabsorbed and absorbed Active Galactic Nuclei (AGNs) out
to z~5. We construct samples containing 2957 sources detected at hard (2-7 keV)
X-ray energies and 4351 sources detected at soft (0.5-2 keV) energies from a
compilation of Chandra surveys supplemented by wide-area surveys from ASCA} and
ROSAT. We consider the hard and soft X-ray samples separately and find that the
XLF based on either (initially neglecting absorption effects) is best described
by a new flexible model parametrization where the break luminosity,
normalization and faint-end slope all evolve with redshift. We then incorporate
absorption effects, separately modelling the evolution of the XLFs of
unabsorbed ($20<\log N_\mathrm{H}<22$) and absorbed ($22<\log N_\mathrm{H}<24$)
AGNs, seeking a model that can reconcile both the hard- and soft-band samples.
We find that the absorbed AGN XLF has a lower break luminosity, a higher
normalization, and a steeper faint-end slope than the unabsorbed AGN XLF out to
z~2. Hence, absorbed AGNs dominate at low luminosities, with the absorbed
fraction falling rapidly as luminosity increases. Both XLFs undergo strong
luminosity evolution which shifts the transition in the absorbed fraction to
higher luminosities at higher redshifts. The evolution in the shape of the
total XLF is primarily driven by the changing mix of unabsorbed and absorbed
populations.
