Аннотация:The physical origin of Type I superluminous supernovae (SLSNe-I), whose luminosities are 10 to 100 times brighter than normal core-collapse supernovae, remains still unknown. Radioactive-decays, magnetars, and circumstellar interactions have been proposed for the power source the light curves, although no definitive conclusions have been reached yet. Since most of light curve studies have been based on simplified semi-analytic models, we have constructed detailed light curve models for various mass of stars including very massive ones and large amount of mass loss with radiation hydrodynamical calculations. Here we focus on the magnetar and circumstellar interaction models and compare their rising time, peak luminosity, width, decline rate of the light curves with observations which show quite a large diversities. We then discuss how to discriminate these models, relevant models parameters, their evolutionary origins, possible roles of chemical enrichment of the early universe, and implications for the identifications of first stars.