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Gravitational waves astronomy promises to reveal to us the nature and structure of black holes and compact stars. This information comes encoded in the waveforms current and future detectors will pick up. Extracting it is well known to be a significant data analysis challenge. Interpreting it, and using it to probe gravity itself and fundamental physics, is a whole different challenge, that involves modelling strong gravity beyond general relativity and/or the standard model. I will give a broad overview of what this entails and discuss future perspectives in this direction.