The character of the first galaxies at redshifts z [greater-than or equal to] 10 strongly depends on the star formation which takes place during their assembly. Conducting cosmological hydrodynamics simulations, we study how the radiative output and chemical enrichment from the first stars impacts the properties of the first galaxies. We find that the radiative feedback from the first stars suppresses the star formation rate at redshifts z [greater-than or equal to] 15 by a factor of only a few. In turn, this suggests that a large fraction of the first galaxies may form from gas which has already been enriched with the first heavy elements ejected by primordial supernovae. In order to characterize the properties of primordial dwarf galaxies, we carry out radiation hydrodynamics simulations which allow to determine how the luminosities in hydrogen and helium emission lines depend on the initial mass function of the stars in the galaxy. As well, we show that the chemical abundance patterns observed in metal-poor Galactic halo stars contain the signature of the first supernovae, and we use this data to indirectly probe the properties of the first stars. / text