Structural models of alkali tellurite glasses, (M2O)(x)(TeO2)(1-x) with M = Li, Na, K are presented. The glass structure was studied with neutron and X-ray diffraction, and, in the case of sodium, NMR. Real-space models of the glass structure were built using the reverse Monte Carlo algorithm. The distribution of polyhedral types as a function of alkaline ion type and composition is derived. It is concluded that the broad distribution of polyhedral species, as compared to that found in crystalline tellurites of similar composition, is responsible for the marked resistance to devitrification shown by these glasses.