  The possibility that spacetime is extended beyond the familiar 3+1-dimensions
has intrigued physicists for a century. Indeed, the consequences of a
dimensionally richer spacetime would be profound. Recently, new theories with
higher dimensional spacetimes have been developed to resolve the hierarchy
problem in particle physics. These scenarios make distinct predictions which
allow for experiment to probe the existence of extra dimensions in new ways. We
review the conceptual framework of these scenarios, their implications in
collider and short-range gravity experiments, their astrophysical and
cosmological effects, as well as the constraints placed on these models from
present data.
