The discovery of the first damped Lyman alpha ( DLA ) system in the early 1970s followed by the recognition that DLAs arise in intervening galaxies opened up a new field of galaxy evolution research . These highest HI column density absorption-line systems trace the bulk of the observed neutral gas in the universe , and therefore , have been used as powerful probes of galaxy formation and evolution back to the redshifts of the most distant quasars . The history and progress of DLA research over the past several decades is reviewed here . Larger datasets and deeper surveys , particularly over the last couple of years , have improved our knowledge of the neutral gas content and distribution in the universe at all observable redshifts , including the present epoch . New results on the statistics of DLAs at z < 1.65 from our HST-UV surveys are presented and discussed in the context of recent results at z = 0 and at high redshift . We find that \Omega _ { DLA } ( z > 0 ) remains roughly constant to within the uncertainties ; the z = 0 value of the neutral gas mass density , \Omega _ { g } , is a factor of \approx 2 less than \Omega _ { DLA } . The DLA incidence , n ( z ) , undergoes rapid evolution between redshifts 5 and 2 , but is consistent with the no-evolution curve in the current concordance cosmology for z \lesssim 2 . We also show that if the local Schmidt law relating surface density of gas and star formation rate ( SFR ) is valid at the DLA redshifts , then the DLA SFR density is too low for them to provide a significant contribution to the cosmic star formation history ( SFH ) at z \gtrsim 1 . This implies that the DLAs are unlikely to be the same population as the star forming galaxies ( i.e. , the Lyman break and sub-millimeter galaxies ) that dominate the SFH of the high redshift universe . We suggest that this discrepancy and the DLA “ missing metals ” problem could be the result of missing very high column density gas due to its very small absorption cross section .