Moonen, Pink, Wedhorn and Ziegler initiated a theory of G-Zips, which is modeled on the de Rham cohomology of varieties in characteristic p>0 “with G-structure”, where G is a connected reductive F_p-group. Building on their work, when X is a good reduction special fiber of a Hodge-type Shimura variety, it has been shown that there exists a smooth, surjective morphism zeta from X to a quotient stack G-Zip^{mu}. When X is of PEL type, the fibers of this morphism recover the Ekedahl-Oort stratification defined earlier in terms of flags by Moonen. It is commonly believed that much of the geometry of X lies beyond the structure of zeta.