The celebrated theorem of Lusternik-Schnirelman states that for any metric on a two-sphere, there are at least three closed embedded geodesics. The corresponding problem for a Riemannian three-sphere asks to find at least four closed embedded minimal two-spheres. The existence of at least one two-sphere was obtained by Simon-Smith in 1983. I’ll explain my joint work with Haslhofer, in which we proved the existence of a second minimal two-sphere. The proof uses many recent developments in min-max theory and mean curvature flow. It is also leads to the existence of minimal non-planar two-spheres in ellipsoids in R^4, answering a question of Yau.