The classification of scalar and vector mesons is reviewed within the framework of the Resonance-Spectrum Expansion (RSE). This method allows a simple and straightforward description of non-exotic meson-meson scattering, incorporating the effects of quark confinement and OZI-allowed decay in a fully nonperturbative way. Results for resonances and bound states are compared to experiment, on the basis of computed pole positions and cross sections. New predictions for open-charm and -bottom scalar mesons are presented. Concretely, observed vector states for uū-dd̄, ss̄, cc̄, and bb̄ are reproduced, and others are predicted. In the light scalar sector, the now established two nonets, one below 1 GeV and one in the region 1.3–1.5 GeV, are easily described, through the appearance of extra poles in the S matrix. The recently found D s0(2317) meson is accurately reproduced by the same mechanism, as a quasi-bound state in the coupled cs̄-DK system. In S-wave Dπ and Bπ scattering, new resonances are foreseen close to threshold, i.e., a D 0 at 2.16±0.05 GeV some 250 MeV wide, and a B 0 at 5.47±0.05 GeV with a width of about 50 MeV. Additional predictions concern the existence of bs̄ and bc̄ scalar mesons, stable with respect to OZI-allowed decay to BK and BD, respectively, namely at 5.61±0.05 GeV resp. 6.64±0.05 GeV.