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Strongly coupled gauge theories and quantum gravity are two of the most important and difficult problems in theoretical physics. Recently, a new connection between these two problems has appeared. It relates string theory in backgrounds that are products of 5-dimensional Anti-de Sitter space times a compact 5-d space to conformally invariant gauge theories in 3+1 dimensions. I will motivate this exact correspondence by considering stacks of large numbers of coincident Dirichlet branes and the curved geometries they create. I will also show how gauge invariant operators of the gauge theory are related to the string theory modes and sketch the method for obtaining correlation functions. Finally, I will describe recent ideas on how to extend the correspondence to non-conformal gauge theories that exhibit confinement and chiral symmetry breaking.