ADM, BMS, and some puzzling interconnections

Abstract The precise connection between the ADM and BMS formalisms is still far from being fully understood. It leads superficially to some puzzles whose resolution can provide new interesting physical insights. One example concerns the claimed local-in-angle conservation of energy in a gravitational scattering process, whose physical meaning I will try to clarify in an explicit example. As my main topic, I will sketch my own understanding of how a recent saga on the definition of angular momentum, its loss, and its radiation, appears to have found its way to a happy ending by appealing to some non-trivial connections between ADM and BMS quantities in asymptotically flat and stationary spacetimes.