 In response to the apparent violation of the Generalized Second Law consequent on Geroch's proposed process, Bekenstein postulated a limit to how much entropy can be contained in a given region of spacetime in order to try to avoid such seeming violations, the limit being given by the entropy of a black hole whose horizon would encompass the region. Current physics imposes no such limit, so Bekenstein (1981) postulated that the limit would be enforced by the underlying theory of quantum gravity that, it is hoped, black hole thermodynamics provides our best current insight into. There is, moreover, a further, related reason that one might think that black hole thermodynamics implies a fundamental upper bound on the amount of entropy that can be contained in a given spacetime region. Suppose that there were more entropy in some region of spacetime than the Bekenstein entropy of a black hole of the same size. Then one could collapse that entropic matter into a black hole, which obviously could not be larger than the size of the original region (or the matter would have already collapsed to form a black hole). But this would violate the Generalized Second Law, for the Bekenstein entropy of the resulting black hole would be less than that of the matter that formed it. Thus the Generalized Second Law itself appears to imply a fundamental limit on how much entropy a region can contain (Bekenstein 1983; Bousso 1999a, 2006). If this is right, it seems to be a deep insight into the fundamental structure of the world, and in particular it should provide an important clue to the nature of an adequate theory of quantum gravity. 