This paper is written to commemorate the sixitieth birthday of Paul Garabedian. As flight speed increased to the point that the flow was dominated by compressibility effects, the focus moved to transonic flow, and it was in this field that Paul Garabedian's contributions were particularly significant. Advances in computing power and numerical algorithms have brought us to the point where compressible flow calculations are routinely performed by a variety of well established methods. Problems associated with the capture of shock waves and contact discontinuities are clearly understood. While discretization procedures suitable for the treatment of complex configurations have been developed, the computing resources required to produce useful answers continue to test the limits of currently available hardware. Automatic local mesh refinement offers a promising avenue for economical improvement of the resolution of features of complex flows. There are widespread efforts underway to develop accurate and reliable methods of predicting viscous compressible flows. Adequate resolution of the boundary layer requires the use of very fine meshes. If computational methods are to be really useful to airplane designers, they must be able to treat extremely complex configurations, ultimately extending up to a complete aircraft. Different strategies that have proved effective in practice are described and a transonic flow calculation for a Boeing 747- 200 is demonstrated as example.