Simulations of the Intergalactic Medium

I present a review by epoch of baryons in the intergalactic medium (IGM), from the first star until today. Recent observations indicate a protracted period of reionization, suggesting multiple populations of reionizers; detection of these z>6 sources is a key goal that is now coming within reach. The optical Lyman alpha forest (2<z<4) is well-described by the Fluctuating Gunn-Peterson Approximation, but puzzling observations of associated metal lines and nearby galaxies may provide insights into galactic feedback processes. IGM studies at z<1.5 are progressing rapidly thanks to ultraviolet absorption line studies of both Ly-alpha absorbers and the warm-hot intergalactic medium. Cosmological hydrodynamic simulations have played an integral part in these advances, and have helped to shape our understanding of the IGM at each epoch. Working jointly, observations and theory continue to expand our knowledge of the IGM as the earliest stages of galaxy formation and the dominant reservoir of baryons at all redshifts.