Imagine there is a way to solve any equations of motion by transforming them into trivial ones. That is what action-angle (AA) coordinates do for Hamiltonian mechanics. Of course, the issue is that by doing so, you just move the problem from solving the equations of motion to finding the transformation. Nevertheless, the transformation to AA coordinates represents an efficient and systematic way to store and represent the solution. Even more, AA coordinates are an extremely useful starting point for perturbation theory of the original equations of motion. In this talk I show how transformations to and from action-angle coordinates can be found for black-hole geodesics and how that simplifies gravitational-wave inspirals both in the extreme and comparable mass ratio regimes.