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The classification of scalar and vector mesons is reviewed within theframework of the Resonance-Spectrum Expansion (RSE). This method allows asimple and straightforward description of non-exotic meson-meson scattering,incorporating the effects of quark confinement and OZI-allowed decay in a fullynonperturbative way. Results for resonances and bound states are compared toexperiment, on the basis of computed pole positions and cross sections. Newpredictions for open-charm and -bottom scalar mesons are presented.  Concretely, observed vector states for u-ubar/d-dbar, s-sbar, c-cbar, andb-bbar 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 - 1.5GeV, are easily described, through the appearance of extra poles in thescattering matrix. The recently found Ds0*(2317) meson is accurately reproducedby the same mechanism, as a quasi-bound state in the coupled c-sbar/DK system.  In S-wave D-pion and B-pion scattering, new resonances are foreseen close tothreshold, i.e., a D0* at 2.16(+-0.05) GeV some 250 MeV wide, and a B0* at5.47(+-0.05) GeV with a width of about 50 MeV. Additional predictions concernthe existence of b-sbar and b-cbar scalar mesons, stable with respect toOZI-allowed decay to BK and BD, respectively, namely at 5.61(+-0.05) GeV resp.6.64(+-0.05) GeV.Comment: review article, 19 pages, plain LaTeX, figures include

CLASSIFICATION OF THE SCALAR MESONS: A STRANGE POLE EXPEDITION INTO CHARM AND BEAUTY TERRITORY