In this talk, I will present decay properties for massless and massive Vlasov fields on the exterior of Schwarzschild spacetimes. In these geometric backgrounds, Vlasov fields are transported along the geodesic flow. An important difficulty of the problem is the existence of trapped geodesics. We deal with these, by using expansion and contraction properties of the geodesic flow. This work is motivated by the study of self-gravitating collisionless systems on black hole exteriors. This is partly based on joint work with Léo Bigorgne (Université de Rennes).