Toric symplectic manifolds have a beautiful description in terms of polytopes. Geometric properties of the manifolds translate to combinatorial properties of the polytope. Not all symplectic manifolds admit such a nice torus action, though. I will describe how symplectic geometers have been using toric degeneration to associate a toric variety (and a polytope) to a non-toric symplectic manifold and what problem they have been able to solve using this technique. I will of course start with a short introduction to symplectic geometry.