The construction and classification of ancient solutions to the Ricci flow is a popular subject in geometric analysis which has arisen out of the need to provide useful models of finite-time singularities of Ricci flow. In this talk, I will discuss classical examples of ancient Ricci flows on spheres which are rotationally-invariant, as well as some more recent constructions of ancient flows on spheres which are invariant under a product of two orthogonal groups.