In this talk,I will first define the integral model of a quaternionic Shimura variety following the strategy of Deligne and Carayol.Then I will explain how to define partial Hasse invariants and Goren-Oort stratification on the special fiber of such varieties.We will prove that each closed GO-stratum is an iterated P1 bundle over the special fiber of another quaternionic Shimura varieties.These geometric results can be used to compute the cohomology of each GO-stratum,and have interesting applications to the classicality of overconvergent p-adic Hilbert modular forms,and the Tate conjecture for Hilbert modular varieites over finite fields.