High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation-propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-annulus computational fluid dynamics can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flow rate. This approach, however, leads to sub-optimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flow rate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.