The classical Hasse invariant is a modular form of weight p-1 in characteristic p which has a simple zero at each supersingular point. In this talk, we will discuss how to generalize the Hasse invariant to unitary Shimura varieties with signature (1,n-1) using the idea of Ekedahl-Oort stratification. We will also discuss an application to the l-adic cohomology of unitary Shimura varieties with bad reduction (Iwahori level structure) using integral models of Harris-Taylor-Yoshida and the weight spectral sequence of Rapoport-Zink.