Summary: Computationally-efficient aerodynamic shape optimisation can be realised using surrogate-based methods. By shifting the optimisation burden to a cheap and yet reasonably accurate surrogate model, the design cost can be substantially reduced, particularly if the surrogate exploits an underlying physics-based low-fidelity model (e.g., the one obtained by coarse-discretisation computational fluid dynamics (CFD) simulation). The knowledge about the physical system of interest contained in the low-fidelity model allows us to construct an accurate representation of the original, high-fidelity CFD model, using a small amount of high-fidelity data and dramatically reduce the overall design cost. Two fundamental issues in such a process are a proper selection of the quality of the low-fidelity model (e.g., the model ’mesh coarseness’ that may affect both the optimisation cost and the reliability of the design process), as well as the scaling properties of the surrogate-based design process with respect to the dimensionality of the design space. Our investigations are carried out for specific variable-resolution optimisation methodologies exploiting two types of correction methods: shape-preserving response prediction and space mapping.