  There is overwhelming evidence for the presence of supermassive black holes
(SMBHs) in the centers of most nearby galaxies. The mass estimates for these
remnant black holes from the stellar kinematics of local galaxies and the
quasar phenomenon at high redshifts point to the presence of assembled SMBHs.
The accretion history of SMBHs can be reconstructed using observations at high
and low redshifts as model constraints. Observations of galaxies and quasars in
the submillimeter, infrared, optical, and X-ray wavebands are used as
constraints, along with data from the demography of local black holes.
Theoretical modeling of the growth of black hole mass with cosmic time has been
pursued thus far in two distinct directions: a phenomenological approach that
utilizes observations in various wavebands, and a semi-analytic approach that
starts with a theoretical framework and a set of assumptions with a view to
matching observations. Both techniques have been pursued in the context of the
standard paradigm for structure formation in a Cold Dark Matter dominated
universe. Here, we examine the key issues and uncertainties in the theoretical
understanding of the growth of SMBHs.
