We present a comparison between the observed properties of damped Lyα systems (DLAs) and the predictions of simple models for the evolution of present-day disc galaxies, including both low and high surface brightness galaxies. We focus, in particular, on the number density, column density distribution and gas density of DLAs, which have now been measured in relatively large samples of absorbers. From the comparison we estimate the contribution of present-day disc galaxies to the population of damped Lyα systems, and how it varies with redshift. Based on the differences between the models and the observations, we also speculate on the nature of the fraction of DLAs that apparently do not arise in disc galaxies.