Peláez Sagredo, José RamónRodas, ArkaitzRuiz de Elvira Carrascal, Jacobo2023-06-172023-06-172021-06-161951-635510.1140/epjs/s11734-021-00142-9https://hdl.handle.net/20.500.14352/8270© 2021 Springer Heidelberg. We acknowledge J.A. Oller for encouraging us to write a tutorial review on this topic. We thank I. Danilkin for his corrections on the manuscript. This project has received funding from the Spanish Ministerio de Ciencia e Innovacion grant PID2019-106080GB-C21 and the European Union's Horizon 2020 research and innovation program under grant agreement No 824093 (STRONG2020). AR acknowledges the financial support of the U.S. Department of Energy contract DE-SC0018416 at William & Mary, and contract DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Lab. JRE acknowledges financial support from the Swiss National Science Foundation under Project No. PZ00P2174228.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.engjournal articlehttp://dx.doi.org/10.1140/epjs/s11734-021-00142-9https://link.springer.com/open access51-73Pion-pion scatteringRigorous absolute boundsPartial-wave amplitudesBethe-salpeter approachQuark-mass dependencePhase-shift analysisLarge-NcKpi scatteringK(k)over-bar scatteringProduction mechanisms.Física-Modelos matemáticosFísica matemática