This work reports the thermodynamic modelling assessment of the rather complex Cs-Mo-O system, which is key for the understanding of fission products chemistry in oxide fuelled Light Water Reactors (LWRs) and next generation Sodium-cooled and Lead-cooled Fast Reactors (SFRs and LFRs). The model accounts for the existence of the ternary molybdates Cs₂MoO₄ (α and β), Cs₂Mo₂O₇ (α and β), Cs₂Mo₃O₁₀, Cs₂Mo₄O₁₃, Cs₂Mo₅O₁₆, and Cs₂Mo₇O₂₂, for which sufficient structural and thermodynamic information are available in the literature. These phases are treated as stoichiometric in the model. The liquid phase is described with an ionic two-sublattice model, and the gas phase as an ideal mixture. The optimized Gibbs energies are assessed with respect to the known thermodynamic and phase equilibrium data in the Cs₂MoO₄-MoO₃ pseudo-binary section. A good agreement is generally obtained within experimental uncertainties. The calculated vapour pressures above Cs₂MoO₄ (solid and liquid) are also compared to the available experimental data. Finally, isotherms of the Cs-Mo-O ternary phase diagram are calculated at relevant temperatures for the assessment of the fuel pin behaviour in LWRs, SFRs and LFRs.