The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is shown that sphericity of subgroup schemes is an open and closed condition over arbitrary base schemes generalizing a result by Knop and Röhrle. Moreover spherical embeddings are classified over arbitrary fields generalizing and simplifying results by Huruguen.