The group IV transition metal borides and carbides, and ternary compounds of these materials are important ultra-high temperature ceramics used in the nuclear and aeronautical industries (hypersonic flight components) due to their very high melting temperatures and material characteristics. For these applications, precise knowledge of the phase stability of materials as a function of composition, temperature and even pressure is required, considering all experimental and accurately modelled properties. We review the modelling and experimental data related to the system B-C-Hf-Zr. This review consists of equilibrium thermodynamics of all binary and ternary systems of these elements, as well as the quaternary system itself. We suggest new experiments and changes to the thermodynamic models, considering also first-principles density functional theory insights.