The problem of determining which symplectic circle actions are Hamiltonian is still open. An obvious necessary condition on a compact manifold is that the action must have fixed points corresponding to the critical points of the Hamiltonian function. McDuff showed that this condition was not in general sufficient by constructing a symplectic six-manifold with a circle action which had fixed points but was not Hamiltonian. However, there are no known examples of symplectic non-Hamiltonian circle actions with isolated fixed points (the fixed point sets in McDuff’s example are tori). It is conceivable then that an action with isolated fixed points is Hamiltonian. This was recently proved by Tolman and Weitsman for semi-free circle actions. We will discuss their methods which use integration in equivariant cohomology and explain how they can be extended to some non-semifree cases.