A good understanding of strong interactions at low energies is key in the precision frontier of Particle and Hadron Physics, since most hadronic observables end up in final states involving pions and kaons, the lightest mesons in the Hadron Spectrum. In particular, the pion–pion and pion–kaon scattering lengths are the lowest energy observables for these interactions, and hence a fundamental quantity for understanding hadron interaction at low energies. In this talk we review the current status of their determination. After discussing the predictions expected from chiral symmetry at different orders in the chiral expansion, we review current experimental and lattice determinations. We then focus on the dispersive determination of pion-pion and pion-kaon interactions, based on the analysis of Roy and Roy-Steiner equation, and continue discussing in detail the current tension between the chiral symmetry and dispersive predicition for the pion-kaon scattering lenthgs. We finish this talk providing an explanation of this disagreement.