We will describe the recent progresses in the computation of four-graviton amplitudes at higher-loop order in maximal supergravity and string theory in various dimensions. We will discuss the constraints from dualities and the extended supersymmetry on the structure of the amplitudes. We will explain that the cross-symmetry of gravity, maximal supersymmetry, and the constraints from higher dimensions play an important role in the improved ultraviolet behaviour of maximal supergravity in four dimensions.