I will first explain how to parametrize some moduli spaces of p-divisible groups (Lubin-Tate spaces) by Bruhat-tits buildings and the p-adic spaces associated to some particular case of Shimura varieties by compactifications of those buildings. I will then explain how to develop a Harder-Narasimhan type theory for finite flat group schemes and p-divisible groups that allows us to develop a "reduction theory" for the action of Heche correspondences acting on more general moduli spaces of p-divisible groups and more general Shimura varieties