  The cosmic reionization of hydrogen was the last major phase transition in
the evolution of the universe, which drastically changed the ionization and
thermal conditions in the cosmic gas. To the best of our knowledge today, this
process was driven by the ultra-violet radiation from young, star-forming
galaxies and from first quasars. We review the current observational
constraints on cosmic reionization, as well as the dominant physical effects
that control the ionization of intergalactic gas. We then focus on numerical
modeling of this process with computer simulations. Over the past decade,
significant progress has been made in solving the radiative transfer of
ionizing photons from many sources through the highly inhomogeneous
distribution of cosmic gas in the expanding universe. With modern simulations,
we have finally converged on a general picture for the reionization process,
but many unsolved problems still remain in this young and exciting field of
numerical cosmology.
