Observations of damped Lyα systems offer a unique window on the neutral-gas reservoirs that gave rise to galaxies at high redshifts. This review focuses on critical properties such as the H I and metal content of the gas and on independent evidence for star formation. Together, these provide an emerging picture of gravitationally bound objects in which accretion of gas from the IGM replenishes gas consumed by star formation. Other properties such as dust content, molecular content, ionized-gas content, gas kinematics, and galaxy identifications are also reviewed. These properties point to a multiphase ISM in which radiative and hydrodynamic feedback processes are present. Numerical simulations and other types of models used to describe damped Lyα systems within the context of galaxy formation are also discussed.