This review summarizes recent studies of the cold neutral hydrogen gas associated with galaxies probed via the HI 21-cm absorption line. HI 21-cm absorption against background radio-loud quasars is a powerful tool to study the neutral gas distribution and kinematics in foreground galaxies from kilo-parsec to parsec scales. At low redshifts (z<0.4), it has been used to characterize the distribution of high column density neutral gas around galaxies and study the connection of this gas with the galaxys optical properties. The neutral gas around galaxies has been found to be patchy in distribution, with variations in optical depth observed at both kilo-parsec and parsec scales. At high redshifts (z>0.5), HI 21-cm absorption has been used to study the neutral gas in metal or Lyman-alpha absorption-selected galaxies. It has been found to be closely linked with the metal and dust content of the gas. Trends of various properties like incidence, spin temperature and velocity width of HI 21-cm absorption with redshift have been studied, which imply evolution of cold gas properties in galaxies with cosmic time. Upcoming large blind surveys of HI 21-cm absorption with next generation radio telescopes are expected to determine accurately the redshift evolution of the number density of HI 21-cm absorbers per unit redshift and hence understand what drives the global star formation rate density evolution.
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