Let $G$ be an even orthogonal group over a $p$-adic local field. Given a parahoric subgroup $K_p$ of $G$ and a minuscule geometric cocharacter $\mu$, one can associate a canonical local model, which is a projective scheme over the ring of $p$-adic integers whose generic fiber is the flag variety attached to $\mu$. When $p>2$ and the triple $(G,K_p,\mu)$ arises from a global Shimura datum, it is known that the local model is étale locally isomorphic to the canonical integral model of the corresponding Shimura variety. In this talk, we focus on the case of PEL type D. We prove that the spin local models introduced by Pappas-Rapoport are isomorphic to the corresponding canonical local models. This confirms a conjecture of Pappas-Rapoport. As a corollary, we obtain an explicit moduli interpretation for flat integral moduli spaces of PEL type D. This talk is partly based on joint work with Ioannis Zachos and Zhihao Zhao.