  Understanding how Active Galactic Nuclei (AGN) evolve through cosmic time
allows us to probe the physical processes that control their evolution. We use
an updated model for the evolution of masses and spins of supermassive black
holes (SMBHs), coupled to the latest version of the semi-analytical model of
galaxy formation GALFORM using the Planck cosmology and a high resolution
Millennium style dark matter simulation to make predictions for AGN and SMBH
properties for $0 < z < 6$. We compare the model to the observed black hole
mass function and the SMBH versus galaxy bulge mass relation at $z=0$, and
compare the predicted bolometric, hard X-ray, soft X-ray and optical AGN
luminosity functions to observations at $z < 6$, and find that the model is in
good agreement with the observations. The model predicts that at $z<2$ and
$L_{\mathrm{bol}} < 10^{43} \mathrm{ergs^{-1}}$, the AGN luminosity function is
dominated by objects accreting in an Advection Dominated Accretion Flow (ADAF)
disc state, while at higher redshifts and higher luminosities the dominant
contribution is from objects accreting via a thin disc or at super-Eddington
rates. The model also predicts that the AGN luminosity function at $z<3$ and
$L_{\mathrm{bol}} < 10^{44} \mathrm{ergs^{-1}}$ is dominated by the
contribution from AGN fuelled by quiescent hot halo accretion, while at higher
luminosities and higher redshifts, the AGN luminosity function is dominated by
the contribution from AGN fuelled by starbursts triggered by disc
instabilities. We employ this model to predict the evolution of SMBH masses,
Eddington ratios, and spins, finding that the median SMBH spin evolves very
little for $0<z<6$.
