Three problems, the specific frequencies, metallicities and mass spectra, in studies of globular cluster systems are reviewed and discussed for current knowledge and open issues. It is noted that different between specific frequencies of globular clusters from galaxies to galaxies indicate  different formation models. The metallicity distributions imply  three probable epochs of globular cluster formation corresponding to three kinds of formation models. The power-law initial mass functions can be physically connected with globular cluster formation even though the preliminary results of simulations with the log-normal initial mass functions are more consistent with current observations.