Hydrogen is the most abundant element in the Universe and neutral hydrogen, HI, is present in virtually all astrophysical structures ranging from the filamentary cosmic web to the inner regions of galaxies to the intracluster medium. The absorption transition from ground state to the lowest excitation state in neutral hydrogen gives rise to the countless optically thin Ly α forest lines and, in the highest column density structures, the damped Ly α absorption lines (DLAs). In optically thick structures, radiative ionization creates sharp “breaks” in quasar spectra called Lyman-limit systems (LLSs). HI correlates with the overdensity of the astrophysical environment, but this relationship evolves with redshift. HI also traces the mass density of neutral gas and the ionization history of the Universe. In this chapter, we describe the cosmic evolution of Ly α absorbers as recorded in quasar spectra from the Epoch of Reionization to the present epoch. At the highest redshifts, the transition from a dense Ly α forest to Ly α spikes to the famous Gunn-Peterson trough is described.