We summarise the results of a major Hubble Space Telescope imaging study of the host galaxies of radio-loud and radio-quiet quasars. We find that for absolute magnitudes M-R < -24 the hosts of both types of quasar are massive elliptical galaxies. By applying the relation between galaxy spheroid mass and black-hole mass derived for nearby inactive galaxies we estimate the masses of the central black holes in the quasars and find the first signs of a difference between radio-loud and radio-quiet objects. The black-hole masses of the radio-loud quasars (RLQs) are systematically larger than those of radio-quiet quasars (RQQs) of similar optical luminosity. The implications of this result for the origins of radio loudness are discussed.