The host galaxies associated with GRBs are observed to have magnitudes R~25. Here we compare the observed redshifts and magnitudes of the host galaxies with the predictions of three basic models: the comoving rate density of GRBs is (1) proportional to the cosmic star formation rate density, (2) proportional to the total integrated stellar density and (3) constant. All models make the assumption that at every epoch the probability of a GRB occuring in a galaxy is proportional to that galaxy's broad-band luminosity. No assumption is made that GRBs are standard candles or even that their luminosity function is narrow. All three rate density models are consistent with the observed GRB host galaxies to date. The fraction of host galaxies fainter than 27 mag may constrain the faint end of the galaxy luminosity function at high redshift, or, if the fraction is observed to be low, may suggest that the bursters are expelled from low-luminosity hosts. In all models, the probability of finding a z<0.008 GRB among a sample of ten GRBs is less than 10^{-4}, strongly suggesting that GRB 980425, if associated with supernova 1998bw, represents a distinct class of GRBs.