I will discuss the Momentum Average approximation -- a simple, highly efficient yet accurate analytical approximation for the Green's function of a Holstein polaron. One way of explaining it is that it corresponds to summing all of the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling, and is accurate everywhere in the parameter space. The resulting Green's function satisfies exactly the first six spectral weight sum rules, and all higher sum rules are satisfied with great accuracy. Comparison with existing numerical data also confirms this accuracy. A systematic way to improve the accuracy of the approximation will then be introduced. Finally, I will briefly discuss generalizations to other models that we have successfully carried out to date.