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.
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