unitary shimura varieties are moduli spaces of abelian varieties with an action of a quadratic imaginary field, and extra structure. in this talk, we'll discuss specific examples of unitary shimura varieties whose supersingular loci can be concretely described in terms of deligne-lusztig varieties. by rapoport-zink uniformization, much of the structure of these supersingular loci can be understood by studying an associated moduli space of p-divisible groups (a rapoport-zink space). we'll discuss the geometric structure of these associated rapoport-zink spaces as well as some techniques for studying them.