Damped Ly-α systems are the major repository of the observed neutral HI at high redshift. These systems are most efficiently detected via absorption spectra taken against distant QSOs. In this paper, we review some of the observational constraints on the nature of these objects, and also discuss the implications of recent observations of two low redshift damped absorbers, made with the Giant Metrewave Radio Telescope. We find that, for the lowest redshift (z = 0.0912) damped Ly-α system, if the system is a rotating gas disk, then the total associated HI mass has to be less than 2 × 10⁹ M⊙, if the disk is at low inclination angles, and less than 10¹⁰ M⊙ if the system is edge on. All limits are 3σ.