The complex flow physics of transonic compressors is linked with strong adverse pressure gradients, shock-wave boundary layer interactions (SBLI) and high level of unsteadiness. These are exacerbated by transitional effects coming along with altitude excitation. This chapter presents implications towards designing more efficient and compact turbomachineries for aeronautics, putting the mechanisms shock wave-boundary layer interactions in the center. Within this scope, a new design solution is proposed, which aims to mitigate limiting effects of transonic speeds at altitude, still maintaining the performance across the operating envelope with a holistic approach. The laminar boundary layer at altitude incurs a multi-shock pattern in the flow with a larger separated region accompanied with high losses and low-frequency unsteadiness. High fidelity numerical approaches are employed to capture the physics of the phenomenon accurately. It is followed by a numerical validation study carried out on a canonical test case, namely the Sandia axisymmetric transonic bump. The captured physics over the transonic, spherical bump is applicable to the flow in transonic compressor passages. Therefore, it is aimed to evaluate the strength and weakness of various numerical methods and different modelling approaches in respect to investigations of shock-boundary layer interaction.