Superluminous supernovae are a new class of supernovae that were recognized about a decade ago. Both observational and theoretical progress has been significant in the last decade. In this review, we first briefly summarize the observational properties of superluminous supernovae. We then introduce the three major suggested luminosity sources to explain the huge luminosities of superluminous supernovae, i.e., the nuclear decay of 56Ni, the interaction between supernova ejecta and dense circumstellar media, and the spin down of magnetars. We compare these models and discuss their strengths and weaknesses.

45 pages, 6 figures, a refereed review article to be published in Space Science Reviews