  In this article, we treat two questions on Rapoport--Zink spaces of Hodge
type constructed by Hamacher and Kim. One of which is their singularities, and
the other is $p$-adic uniformization of Shimura varieties. More precisely, we
prove that the singularity of a Rapoport--Zink space is controlled by its
asssociated local model, and the basic locus of a Kisin--Pappas integral model
of a Shimura variety is uniformized by the corresponding Rapoport--Zink space.
These results extend the known facts by Rapoport and Zink in the case of PEL
type.
