It has been known for over a century that there are many Riemannian metrics on the 2-sphere with the property that all of their geodesics are closed. Zoll constructed an infinite dimensional family of surfaces of rotation with this property and, following ideas of Funk, Guillemin proved that these metrics on the 2-sphere are essentially parametrized by the odd functions on the round 2-sphere. However, this existence proof does not give explicit examples. A different approach is to ask for metrics on the 2-sphere whose geodesic flows have `local conservation laws', as does the ellipsoid (after the famous analysis of Jacobi). This approach leads to the construction of an infinite series of explicit families of metrics on the 2-sphere with all geodesics closed, most of which have no continuous symmetries. These ideas can also be applied to the understanding of Finsler metrics on the 2-sphere whose Finsler-Gauss curvature is constant, as will be explained in the talk.