%0 Journal Article %A Peláez Sagredo, José Ramón %A Rodas, Arkaitz %A Ruiz de Elvira Carrascal, Jacobo %T Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances sigma/f(0)(500) and kappa/K*(0)(700) %D 2021 %@ 1951-6355 %U https://hdl.handle.net/20.500.14352/8270 %X For several decades, the sigma/f(0)(500) and kappa/K*(0)(700) resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review, we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons sigma/f(0)(500) and kappa/K*(0)(700). Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats. %~