Damped Lyman-α systems (DLAs) are useful probes of star formation and galaxy formation at high-redshift (hereafter high-z). We study the physical properties of DLAs and their relationship to Lyman break galaxies (LBGs) using cosmological hydrodynamic simulations based on the concordance Λ cold dark matter model. Fundamental statistics such as global neutral hydrogen (H I) mass density, H I column density distribution function, DLA rate-of-incidence and mean halo mass of DLAs are reproduced reasonably well by the simulations, but with some deviations that need to be understood better in the future. We discuss the feedback effects by supernovae and galactic winds on the DLA distribution. We also compute the [C II] emission from neutral gas in high-z galaxies, and make predictions for the future observations by the Atacama Large Millimeter Array (ALMA) and Space Infrared Telescope for Cosmology and Astrophysics (SPICA). Agreement and disagreement between simulations and observations are discussed, as well as the future directions of our DLA research.