On perturbative gravity and gauge theory

We review some applications of tree-level (classical) relations between gra vity and gauge theory that follow from string theory. Together with D-dimen sional unitarity, these relations can be used to perturbatively quantize gr avity theories, i.e. they contain the necessary information for obtaining l oop contributions. We also review recent applications of these ideas showin g that N = 1 D = II supergravity diverges, and review arguments that N = 8 D = 4 supergravity is less divergent than previously thought, though it doe s appear to diverge at five loops. Finally, we describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relatio nship between gravity and gauge theory.