At epochs corresponding to z ~ 1000, the IGM is expected to recombine and remain neutral until sources of radiation develop that are capable of reionizing it. The detection of transmitted flux shortward of the Ly wavelength in the spectra of sources at z ~ 5 implies that the hydrogen component of this IGM was ionized at even higher redshifts. There is some evidence that the double reionization of helium may have occurred later, but this is still controversial. It appears then that substantial sources of ultraviolet photons were already present when the Universe was less than 7% of its current age, perhaps quasars and/or young star-forming galaxies: an episode of pre-galactic star formation may provide a possible explanation for the widespread existence of heavy elements (like carbon, oxygen, and silicon) in the IGM, while the integrated radiation emitted from quasars is likely responsible for the reionization of intergalactic helium. Establishing the epoch of reionization and reheating is crucial for determining its impact on several key cosmological issues, from the role reionization plays in allowing protogalactic objects to cool and make stars, to determining the small-scale structure in the temperature fluctuations of the cosmic background radiation. Conversely, probing the reionization epoch may provide a means for constraining competing models for the formation of cosmic structures, and of detecting the onset of the first generation of stars, galaxies, and black holes in the Universe.