The textbook advantages of high-order differencing schemes in computational fluid dynamics (CFD) are well documented. They have also been demonstrated in the literature, albeit for canonical problems. The objective of the work described in this paper is to provide a robust implementation of high-order schemes to permit high fidelity and routine simulation of realistic aerospace systems which usually involve very complex geometries and flow behaviors. The two high-order schemes we have implemented are the compact and weighted essentially non-oscillatory (WENO) schemes. Some challenges were encountered in our efforts to accomplish the foregoing objective. Detailed illustrations of the various challenges are provided, as are some remedies that we have proposed and successfully implemented. This then allows us to illustrate some of the potential advantages of high-order methods for the simulation of realistic aerospace applications. The roles that the authors envision for high-order methods in CFD simulation of realistic aerospace systems are also discussed.