We investigate the evolution of damped Ly$\alpha$ absorption systems (DLA) from hierarchical structure formation models by exploring the basic properties of DLA host-galaxies (DLA galaxies) to clarify the connection between DLAs and galaxies. We find that DLA galaxies primarily consist of low surface brightness dwarf galaxies. For example, at redshift $z \le 1$, DLA galaxies have typical radius 3 kpc, surface brightness 22–27 mag arc-sec$^{-2}$, and star formation rate $10^{-2}$ M$_{\odot}$/yr. We discuss selection effects in the detection in emission caused by compactness and brightness. Finally, we explore the radio properties at $z=0$ by comparing the observational results from blind radio surveys.