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In this talk, I will discuss theoretical mechanisms through which different dark matter structures can develop in strong-field regimes, and how current and upcoming gravitational-wave observations can be used to probe them. I will also present the results of the first dedicated search for the imprints of light scalar fields on LIGO–Virgo–KAGRA black hole binaries. Interestingly, the event GW190728 shows a Bayes factor of ln B ~ 3.5 favoring the presence of a superradiant scalar with mass ~ 10^{-12} eV. While this constitutes only a tentative hint rather than conclusive evidence, it illustrates the growing power of gravitational-wave observations to test fundamental physics.