Unified theories suggest that space is intrinsically 10 dimensional, even though everyday phenomena seem to take place in only 3 large dimensions. In “Brane World” models, matter and radiation are localized to a “brane” which has a thickness less than ≈(TeV)−1in all but the usual three dimensions, while gravity propagates in additional dimensions, some of which may extend as far as submillimeter scales. A brief review is presented of some of these models and their astrophysical phenomenology. One distinctive possibility is a gravitational wave background originating in the mesoscopic early universe, at temperatures above about 1 TeV and on scales smaller than a millimeter, during the formation of our 3-dimensional brane within a 10-dimensional space. ©2001 American Institute of Physics.