This review paper deals with the glass formation in molybdate systems and their structure. The molybdate glasses have been mainly of academic interest as model objects in relation to the fundamental questions of the glassy state. On the other hand, these glasses posses a variety of specific properties, and now some of them are potential candidates for technological applications: amorphous semiconductors, waste storage, infrared transmission components, nonlinear optical devices, sensors, reflecting windows, etc. The purpose of this paper is to present a survey of recent results obtained by our research team and by other authors. The main difficulties in the preparation of molybdate glasses are connected with the high crystallisation tendency of the compositions because MoO3 is not able to form a glass itself at slow cooling rates. Molybdate glasses have been obtained by our team introducing different kind of components: modifiers Me2O, MeO), glass network formers (B2O3), transition metal oxides V2O5, Fe2O3, WO3, CuO), heavy metal oxides (Bi2O3, PbO), rare earth oxides (La2O3, Nd2O3, Pr2O3, Sm2O3, Y2O3)The molybdate layer structure is destroyed during vitrification (changes of the middle range order) and mainly octahedral units, which are corner or edge shared, build up the network of the glass compositions with high MoO3 content. Partial MoO6 to MoO4 transformations take place (changes in the short range order). When the amount of MoO4 tetrahedra without oxygen bridging bonds between them reaches a critical concentration, the glass formation ability drastically deteriorates. The Zachariasen's rules about participation of the polyhedra with small coordination number (tetrahedra) are not satisfied for these glasses. The glass structure was compared with that of crystalline phases separated during the heat treatment of the amorphous samples or by the obtained crystals from supercooled melts. The achieved results are directed for the development of novel low melting glasses containing sufficient amount of transition or rare earth metal ions.