  A major goal of observational and theoretical cosmology is to observe the
largely unexplored time period in the history of our universe when the first
galaxies form, and to interpret these measurements. Early galaxies dramatically
impacted the gas around them in the surrounding intergalactic medium (IGM) by
photoionzing the gas during the Epoch of Reionization (EoR). This epoch likely
spanned an extended stretch in cosmic time: ionized regions formed and grew
around early generations of galaxies, gradually filling a larger and larger
fraction of the volume of the universe. At some time -- thus far uncertain, but
within the first billion years or so after the big bang -- essentially the
entire volume of the universe became filled with ionized gas. The properties of
the IGM provide valuable information regarding the formation time and nature of
early galaxy populations, and many approaches for studying the first luminous
sources are hence based on measurements of the surrounding intergalactic gas.
The prospects for improved reionization-era observations of the IGM and early
galaxy populations over the next decade are outstanding. Motivated by this, we
review the current state of models of the IGM during reionization. We focus on
a few key aspects of reionization-era phenomenology and describe: the redshift
evolution of the volume-averaged ionization fraction, the properties of the
sources and sinks of ionizing photons, along with models describing the spatial
variations in the ionization fraction, the ultraviolet radiation field, the
temperature of the IGM, and the gas density distribution.
