The damped Lyman-α absorption-line systems (DLAs) that are observed in quasar spectra arise in neutral-gas-rich regions of intervening galaxies. With the highest neutral hydrogen column densities observed (N(HI) ⩾ 2 × 1020 atoms cm−2), they are known to trace the bulk of the neutral gas content of the Universe, and are thus powerful probes of galaxy formation and evolution. However, DLAs are extremely rare, and since the Lyman-α line falls in the UV for redshifts z < 1.65, not many are known at low redshift due to the limited availability of space data. Our HST surveys for DLAs in strong MgII absorbers have been successful at showing that MgII can be used as an unbiased tracer of DLAs. We present new results on their incidence, or redshift number density, dn/dz, and cosmological neutral gas mass density, ΩDLA, at redshifts 0.11 ⩽ z ⩽ 1.65, and incorporate results from higher and lower redshift studies in the literature to derive the evolution of neutral gas in the Universe.