In this talk, we first review the development of conical metrics on compact Riemann surfaces. We then show that on any compact Riemann surface, a reducible spherical conical metric can be partitioned into finitely many pieces by cutting along suitable geodesics, each of which is isometric to a football. As an application, we provide a new proof of the angle constraint for such metrics. This is joint work with Professors Yingyi Wu and Bin Xu.