Over the past two decades high-fidelity simulations have become feasible for most main gas path turbomachinery components. This paper introduces the key challenges of simulating and modelling turbomachinery flows and presents an overview of possible simulation strategies. A comprehensive overview is given of which particular design challenges have to date been addressed by high-fidelity simulations, with a particular focus on high-pressure and centrifugal compressors, and high-pressure and low-pressure turbines. Recommendations are provided for how quality and accuracy can be ensured for high-fidelity simulations, using direct numerical simulations of a low-pressure turbine as a case study. It is argued that industrial impact from high-fidelity simulations can be achieved in two ways, either by conducting design-of-experiment-like studies that can provide designers with insight into certain physical mechanisms and phenomena, or by helping mature and improve lower-order models. The latter is discussed with particular emphasis on recent advances in machine learning for model assessment and improvement, and the potential of one selected data-driven approach is demonstrated on predictions of wake mixing for low-pressure and high-pressure turbines.