The closed gas cycle based on supercritical carbon dioxide (sCO2) is a promising solution to realize highly efficient power systems arranged in compact devices. However, the technical feasibility of these so-called sCO2 power systems relies on the development of non-conventional components, whose features are dictated by the peculiar character of the working fluid. The compressor is a key component of the system and its design demands the set-up of novel guidelines, due to the nearcritical thermodynamic condition of the fluid, which (i) makes the machine operate with a very low flow function, (ii) experiences steep changes in properties across the machine, and (iii) is prone to phase-change in the intake part of the machine. In this study we revise the entire design workflow of a prototype sCO2 centrifugal compressor, from the preliminary definition of the machine, to the mean-line design, and finally to the detailed definition of the meridional channel and of the blade shape, highlighting the aspects making the machine alternative to conventional ones. The compressor aerodynamics is then analyzed by resorting to a high-fidelity Computational Fluid Dynamics (CFD) model in both design and off-design conditions, considering three speed-lines and low/high flow rate margins. Results show the capabilities and limitations of conventional low-fidelity design procedures for designing sCO2 compressors, especially at off-design conditions, and shed light on the technical implications of the thermodynamic character of the fluid, especially in connection to the onset of phase change in the intake region of the impeller and in the tip clearance.