Demands for restitution of 'cultural property' have become increasingly insistent in recent decades. The campaign of the Greek government for the return of the Elgin (or Parthenon) Marbles is well known, but there are many other examples. In this paper Janna Thompson argues that there is a plausible conception of cultural property which can be used to justify some restitution claims. But many demands for restitution (including, she contends, the Greek claim to the Parthenon Marbles) cannot be so justified.