The evolution of the science and art of numerical simulation of complex, complicated fluid flows has made enormous strides in the past forty years. We have progressed from relatively simplified one-dimensional steady-state results to fully three-dimensional, time-dependent simulations including very complex physics. These advances have been driven by new computational hardware, new algorithms for solving the equations, and the real need for this technology. This lecture emphasizes the broad range of applications that are possible and describes some of what we can now do, what we have learned, and where we might go with this exciting technology in the future.