Dispersion relations and the light-hadron spectrum

Light hadron spectroscopy sits in the non‑perturbative regime of QCD, where flexible fits often compete with firm principles. Over the past two decades, dispersion relations have become a practical, numerical tool to solve these issues, enabling first-principles analyses and delivering robust resonance parameters. With $\pi\pi$ scattering as an example, we briefly summarize the current landscape, highlight dispersive work that has resolved long-standing debates and set precision standards, and include recent examples of dispersive analyses of lattice QCD results.