Comprehensive understanding of propulsive jet aerodynamics and aeroacoustics is key to engine design for reduced jet noise and infra-red signature in civil and military aerospace, respectively. Illustrated examples are provided of other aerodynamic/aeroacoustic problems involving jet development, including chevron nozzles, increased jet/wing/flap interference (as fan diameter increases), high acoustic environment (and potentially damaging screech) of supersonic jets on carrier decks and the strongly Three-Dimensional (3D) unsteady flow during the in-ground effect operation of Short Take-Off and Vertical Landing (STOVL) aircraft. To date, laboratory/rig test measurements have primarily been used to identify design solutions; increased use of Computational Fluid Dynamics (CFD) would help achieve cost/time reductions, but Reynolds-Average Navier–Stokes (RANS) CFD with statistical turbulence modelling has proven inadequate for such flows. The scenarios described are far removed from flows used to calibrate model constants, and predictive accuracy demands detailed insight into unsteady flow. Large-Eddy Simulation (LES), whilst computationally more demanding, offers a potential solution. Research undertaken to assess LES capability to address the challenges described is reviewed here. This demonstrates that tremendous progress has been made, indicating that LES can provide sufficiently accurate predictions, representing high value for engineering design. A series of validation studies of increasing realism to practical engineering systems is presented to underpin this conclusion. Finally, areas for further work are suggested to support the combined application of RANS and LES that is probably the optimum way forward.