  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 ~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 ~< 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 >~ 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. (abridged)
