Recent developments in numerical tools for turbomachinery design have made practical the use of gradient-based optimization using high-fidelity computational fluid dynamic (CFD) simulations. Such has been made possible with the use of adjoint solvers, that can efficiently provide the gradients of the functions of interest with respect to the design variables required by the optimizer, at a cost almost independent of the number of variables. The derivation and implementation of the discrete adjoint solver for a legacy Reynolds Average Navier–Stokes (RANS) CFD solver are briefly explained. The adjoint-based gradients of some functions of interest, such as mass flow, pressure ratio and efficiency, with respect to shape parameters are computed and benchmarked against finite-difference approximations and excellent agreement is demonstrated. The outline of the integration of such adjoint tool in an engineering design framework is presented and discussed. The adjoint-based design framework is tested on a shape optimization problem using a set of Hicks-Henne bump functions superimposed on the baseline shape as design variables. A simple design problem is presented: a compressor rotor blade passage is setup as an unconstrained maximization problem, where the efficiency is increased by tweaking the camberline angle distribution.