Sudden changes in the internal structure of stars, placed at the interface between convective and radiative regions, regions of partial ionisation, or between layers that have acquired different chemical composition as a result of nuclear burning, often produce specific signatures in the stars oscillation spectra. Through the study of these signatures one may gain information on the physical processes that shape the regions that produce them, including diffusion and chemical mixing beyond the convectively unstable regions, as well as information about the helium content of stars. In this talk, I will review important theoretical and observational efforts conducted over the years towards this goal. I will emphasise the potential offered by the study of acoustic, gravity, and mixed modes observed in stars of different mass and evolutionary stages, at a time when space-based data is allowing us to build on the knowledge gained from the study of the sun and white dwarfs, where these efforts have long been undertaken, extending the methods developed to stars across the HR diagramme.
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