Supergravity theories were once hoped to provide ultraviolet finite theories of quantum gravity without requiring profoundly new physical frameworks. These hopes faded in the 1980s, but renewed efforts in recent years have uncovered some surprising ultraviolet behaviour. In this talk, I will give an overview of the explicit scattering amplitude calculations in perturbative supergravity over the last few years. In particular cases, there are indications of ultraviolet cancellations not accounted for by known symmetry arguments. I will highlight these cases and give some reasons to be optimistic and some reasons to be pessimistic about supergravity as a contender for a quantum theory of gravity.