Closed Joule–Brayton cycles operating with carbon dioxide in supercritical conditions (sCO2) are nowadays collecting a significant scientific interest, due to their high potential efficiency, the compactness of their components, and the flexibility that makes them suitable to exploit diverse energy sources. However, the technical implementation of sCO2 power systems introduces new challenges related to the design and operation of the components. The compressor, in particular, operates in a thermodynamic condition close to the critical point, whereby the fluid exhibits significant non-ideal gas effects and is prone to phase change in the intake region of the machine. These new challenges require novel design concepts and strategies, as well as proper tools to achieve reliable predictions. In this study, we consider an exemplary sCO2 power cycle with the main compressor operating in proximity to the critical point, with an intake entropy level of the fluid lower than the critical value. In this condition, the phase change occurs as evaporation/flashing, thus resembling cavitation phenomena observed in liquid pumps, even though with specific issues associated with compressibility effects occurring in both the phases. The flow configuration is therefore highly nonconventional and demands the development of proper tools for fluid and flow modeling, which are instrumental for the compressor design. The paper discusses the modeling issues from the thermodynamic perspective, then highlighting their implications on compressor aerodynamics. We propose tailored models to account for the effect of the phase change in 0D mean-line design tools as well as in fully three-dimensional (3D) computational fluid-dynamic (CFD) simulations: the former was previously validated for sCO2 compressors, the latter is validated in this paper against experiments of compressible flows of supercritical sCO2 in nozzles. In this way, a strategy of investigation is built-up as a combination of mean-line tools, industrial design experience, and CFD for detailed flow analysis. The investigation reveals that the potential onset of the phase change might alter significantly the performance and operation of the compressor, both in design and in off-design conditions, according to three main mechanisms: incidence effect, front-loading, and channel blockage.