Naturally reductive Riemannian homogeneous spaces and real hypersurfaces in complex and quaternionic space forms J\"urgen Berndt and Lieven Vanhecke Abstract. We prove that the $\eta$-umbilical real hypersurfaces in non-flat complex space forms and the $Q$-quasiumbilical real hypersurfaces in non-flat quaternionic space forms are equipped with a naturally reductive homogeneous structure. Moreover, we show that all simply connected, non-symmetric, three-dimensional naturally reductive Riemannian homogeneous spaces can be realized via standard models of $\eta$-umbilical real hypersurfaces in complex projective and hyperbolic spaces of complex dimension two. Keywords. Complex and quaternionic space forms, $\eta$-umbilical and $Q$-quasiumbilical real hypersurfaces, naturally reductive homogeneous spaces and structures. MS classification. 53B20, 53C30, 53C40, 53C55.