The generalized double copy and its applications to UV properties of supergravity theories.

<!--HTML--><p>Recent years have seen enormous progress in our ability to compute elementary-particle scattering processes in quantum field theory. &nbsp;We will describe the application of modern ideas, including the duality between color and kinematics and advanced loop-integration methods, to studies of the ultraviolet properties of quantum gravity theories. &nbsp;We also describe "enhanced ultraviolet cancellations" for which no standard symmetry explanation has been found, and present the nontrivial example of N = 5 supergravity at four loops.&nbsp;We also show recent results for N = 8 supergravity at five loops, proving that although it is still remarkably well behaved, its behavior is worse than that of N = 4 super-Yang-Mills theory. New structures that should enormously simplify future computations at six loops and beyond will be described. &nbsp;We will also outline recent progress towards applying some of the ideas used in multiloop quantum gravity calculations to the problem of computing classical gravitational radiation from astronomical sources.</p>