I review the physical properties of pair-production supernovae (PPSNe) as well as the prospects for them to be constrained observationally. In very massive (140-260 solar mass) stars, much of the pressure support comes from the radiation field, meaning that they are loosely bound, with an adiabatic coefficient that is close to the minimum stable value. Near the end of C/O burning, the central temperature increases to the point that photons begin to be converted into electron-positron pairs, softening gamma below this critical value. The result is a runaway collapse, followed by explosive burning that completely obliterates the star. While these explosions can be up to 100 times more energetic that core collapse and Type Ia supernovae, their peak luminosities are only slightly greater. However, due both to copious Ni-56 production and hydrogen recombination, they are brighter much longer, and remain observable for ~ 1 year. Since metal enrichment is a local process, PPSNe should occur in pockets of metal-free gas over a broad range of redshifts, greatly enhancing their detectability, and distributing their nucleosyntehtic products about the Milky Way. This means that measurements of the abundances of metal-free stars should be thought of as directly constraining these objects. It also means that ongoing supernova searches, already provide weak constraints for PPSN models. A survey with the NIRCam instrument on JWST, on the other hand, would be able to extend these limits to z ~ 10. Observing a 0.3 deg^2 patch of sky for one week per year for three consecutive years, such a program would either detect or rule out the existence of these remarkable objects.