Recently, there have been remarkable progresses on the analysis of the multi-loop amplitudes in supergravity in various dimensions using string theory and in field theory methods.
There are strong indications that four-dimensional maximal supergravity theories have a better ultraviolet behaviour than expected from a conservative implementation of on-shell superspace.
The pure spinor formalism allowed us to make concrete predictions for the structure of higher-loop four-graviton amplitudes that have been confirmed so far by all explicit field theoretic amplitude computations.
As well beside the constraints from supersymmetry, the amplitudes in colorless gauge theories have a much more simple structure than guessed from a traditional approach based on a Lagrangian and Feynman graphs formalism.
We wil explain how a string based approach makes obvious fundamental cancellations in colorless gauge amplitudes, leading to the no-triangle property of N=8 supergravity one-loop amplitude.