About a fifth of the exoplanetary systems that have been discovered contain a so-called hot-Jupiter – a giant planet orbiting within 0.1 AU of the central star. Since these stars are typically of the F/G spectral type, the orbits of any terrestrial planets in their habitable zones at ~1 AU should be dynamically stable. However, because hot-Jupiters are thought to have formed in the outer regions of a protoplanetary disc, and to have then migrated through the terrestrial planet zone to their final location, it is uncertain whether terrestrial planets can actually grow and be retained in these systems. In this paper we review attempts to answer this question. Initial speculations, based on the assumption that migrating giant planets will clear planet-forming material from their swept zone, all concluded that hot-Jupiter systems should lack terrestrial planets. We show that this assumption may be incorrect, for when terrestrial planet formation and giant planet migration are simulated simultaneously, abundant solid material is predicted to remain from which terrestrial planet growth can resume.