Interest in low Reynolds number compressible flows is emerging due to prospective applications like flight on Mars and in the stratosphere. However, very little knowledge is available, both regarding the flow physics underlying this unique regime and the accuracy of numerical methods for its prediction. In this paper, low and high fidelity numerical approaches are compared with experimental measurements on both airfoils and rotors in the low Reynolds number compressible flow regime. It is shown that low fidelity approaches are suited to aerodynamic optimization despite high viscous and compressible effects. In addition, high fidelity approaches help reveal unique flow features of this regime.