Turbulence has been the subject of intense study for more than one hundred years, and is often called the last important unsolved problem of classical physics. But what is the problem? Why is it so difficult to solve? And why work so hard to solve it? Is it possible that with ever increasing computational capabilities the problem will be bypassed before being solved? In answering these questions, I will suggest that, while advances in computational capabilities over the next decades may allow fundamental advances, understanding, not raw computer power, will remain the essential solution ingredient. Simulations will not be able to achieve robust solutions in astrophysical and geophysical settings without an underlying turbulence model. I will report on recent progress that may point a way forward, including success in modeling turbulent scalar transport using mixed Eulerian/Lagrangian statistics in a simple analog flow. The method maintains essential phase relationships introduced by the presence of coherent flow structures, can reproduced the expectation value of the concentration as function of time and distance from a source using only the statistical properties of the flow, and may prove to be a way to model the important non-diffusive transport properties of turbulence without directly resolving the small scale flows.