Among transition metal carbides and nitrides, zirconium, and hafnium compounds are the most stable and have the highest melting temperatures. Here we review published data on phases and phase equilibria in Hf-Zr-C-N-O system, from experiment and ab initio computations with focus on rocksalt Zr and Hf carbides and nitrides, their solid solutions and oxygen solubility limits. The systematic experimental studies on phase equilibria and thermodynamics were performed mainly 40–60 years ago, mostly for binary systems of Zr and Hf with C and N. Since then, synthesis of several oxynitrides was reported in the fluorite-derivative type of structures, of orthorhombic and cubic higher nitrides Zr3N4 and Hf3N4. An ever-increasing stream of data is provided by ab initio computations, and one of the testable predictions is that the rocksalt HfC0.75N0.22 phase would have the highest known melting temperature. Experimental data on melting temperatures of hafnium carbonitrides are absent, but minimum in heat capacity and maximum in hardness were reported for Hf(C,N) solid solutions. New methods, such as electrical pulse heating and laser melting, can fill the gaps in experimental data and validate ab initio predictions.