The interactions of pions and kaons are of relevance to understand low-energy QCD but also for the description of final state interactions in many other processes of interest for theory and experiment. Unfortunately scattering data is plagued with large systematic uncertainties leading to inconsistent data sets.
We show how stringent dispersion theory constraints lead to a consistent and precise description of meson meson scattering in the region below 2 GeV. Simple parameterizations are provided that can be used later for further theoretical and experimental studies. Dispersion theory can also determine the existence of the controversial light scalar resonances, like the sigma and kappa mesons, and provide presice determinations of their parameters.