39 galaxies are now known, from follow-up of faint IRAS sources and from submm observations of high redshift AGN, with far infrared luminosities > 10^{13} Lo. 13 of these, which have been found in 60 or 850 mu surveys, form an important unbiased sub-sample. 12 have been found by comparison of 60 mu surveys with quasar or radio-galaxy catalogues, or from infrared surveys with colour selection biased towards AGN, while a further 14 have been found through submm observations of known high redshift AGN. In this paper I argue, on the basis of detailed modelling of the spectral energy distributions of hyperluminous galaxies with accurate radiative transfer models, and from evidence of high gas-mass in several cases, that the bulk of the emission from these galaxies at rest-frame wavelengths >= 50 mu is due to star formation. Even after correction for the effects of lensing, hyperluminous galaxies with emission peaking at rest-frame wavelengths >= 50 mu are therefore undergoing star-formation at rates > 1000 Mo/yr and are strong candidates for being primeval galaxies, in the process of a major episode of star formation.