Rapoport and Zink have introduced a family of moduli problems of $p$-divisible groups with additional structure of PEL-type, which they prove to be representable by locally noetherian formal schemes over the ring of $p$-adic integers. In joint work with G. Pappas we give an alternative approach to these spaces, by using moduli spaces of G-displays. This allows to treat the Hodge type analog of these spaces, which was also considered by W. Kim.