  [Abriged] Supermassive black holes (SMBH) lurk in the nuclei of most massive
galaxies, perhaps in all of them. The tight observed scaling relations between
SMBH masses and structural properties of their host spheroids likely indicate
that the processes fostering the growth of both components are physically
linked, despite the many orders of magnitude difference in their physical size.
This chapter discusses how we constrain the evolution of SMBH, probed by their
actively growing phases, when they shine as active galactic nuclei (AGN) with
luminosities often in excess of that of the entire stellar population of their
host galaxies. Following loosely the chronological developments of the field,
we begin by discussing early evolutionary studies, when AGN represented beacons
of light probing the most distant reaches of the universe and were used as
tracers of the large scale structure. This early study turned into AGN
"Demography", once it was realized that the strong evolution (in luminosity,
number density) of the AGN population hindered any attempt to derive
cosmological parameters from AGN observations directly. Following a discussion
of the state of the art in the study of AGN luminosity functions, we move on to
discuss the "modern" view of AGN evolution, one in which a bigger emphasis is
given to the physical relationships between the population of growing black
holes and their environment. This includes observational and theoretical
efforts aimed at constraining and understanding the evolution of scaling
relations, as well as the resulting limits on the evolution of the SMBH mass
function. Physical models of AGN feedback and the ongoing efforts to isolate
them observationally are discussed next. Finally, we touch upon the problem of
when and how the first black holes formed and the role of black holes in the
high-redshift universe.
