Fused yttrium-alumoborate glasses doped with ytterbium, silicon, chromium, and sodium were synthesized. The influence of the matrix on the "spectroscopic behavior" of chromium ions and the efficiency of their sensitization of Yb3+ luminescence was established by spectral-luminescence and EPR-studies. It was found that (1) chromium in alkali-free glasses is mainly in the oxidation degree Cr(III) with an appreciable admixture of Cr(IV) and Cr(V), (2) the partial replacement of Al2O3 or B2O3 by SiO2 and Y2O3 by Yb2O3 affects to a different extent the relative concentration of optical centers of chromium ions, (3) the addition of alkali results in the formation of Cr(VI) centers as a result of oxidation of less charged chromium ions and predominantly tetracoordinated Cr4+ and Cr5+, (4) Cr3+ ions make the main contribution to the luminescence sensitization of Yb3+ ions, while Cr4+ ions and to a lesser extent Cr5+ play the role of luminescence quencher and internal filter. Sensitization of Yb3+ luminescence through the charge transfer band in Cr(VI) was found. An alkaline glass doped with Cr and Yb upon excitation through the sensitizer produced a luminescence quantum yield of 32% and the conditions for its enhancement were considered. It is shown that the temperature quenching of luminescence of CrYb-containing glasses is significantly lower than that of Cr-containing glasses.