A small fraction of supernovae appear much brighter--for a given distance--than typical events. Included among these are so-called ʺsuperluminous supernovaeʺ (SLSNe), which have intrinsically high luminosities. Some other supernovae with normal luminosities may also appear unusually bright due to physical processes external to the supernova. In this talk, I will first introduce SLSNe and describe my recent work in the field. Then I will discuss a recently discovered supernova, PS1-10afx, that appears as bright or even brighter than a SLSN would given its high redshift (z ~ 1.4), but which cannot be explained by any SLSN model. I will show that PS1-10afx is not intrinsically luminous; rather, it is the first discovery of a supernova strongly magnified by a foreground object.