A spherical surface is a surface that can be glued from a collection of spherical triangles by isometric identification of their sides. Such a surface has a metric of curvature one outside of a finite number of points, where the metric has a conical singularity. In particular, each spherical surface is naturally a Riemann surface. Contrary to the hyperbolic case, when the theory is identical to the theory of Riemann surfaces, the case of spherical surfaces is almost totally open. I will speak about recent results in the area, such as a full description of the moduli space of spherical metrics with one conical singularity on a torus (joint work with Gabrielle Mondello and Alex Eremenko) and the description of possible conical angles on a spherical metric on a 2-sphere (joint work with Gabirelle Mondello).