It is a classical problem in geometry to construct interesting metrics on spheres. Sasaki-Einstein metrics are the analogous of Kähler-Einstein metrics for odd dimensional real manifolds. I will report on a joint work with Yuchen Liu and Taro Sano in which we construct infinitely many Sasaki-Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, proving in this way conjectures of Boyer-Galicki-Kollár and Collins-Székelyhidi. The construction is based on showing the K-stability of certain Fano weighted orbifold hypersurfaces.