Unitary Shimura varieties are moduli spaces of abelian varieties with certain extra structures. A fruitful way to study their geometry is by considering stratifications of the space. One such stratification is the Ekedahl-Oort (E-O) stratification defined with respect to the structure of the p-torsion group scheme. We follow the work of Moonen and Wooding to investigate the interaction of the E-O strata with other aspects of the geometry of the Shimura variety. We present a few novel results and observations in some specific cases, as well as some future directions. Time permitting, we'll also talk about the Newton stratification.