In this talk, I will talk about geometric structures and structure-preserving methods for some mathematical models in plasma physics. Specifically, I will introduce the discovery of the Poisson structures of a Vlasov–Maxwell model for laserplasma interaction and spin Vlasov–Maxwell dynamics. Based on these geometric Structures, two kinds of structure-preserving methods are constructed: Eulerian methods and Particle-in-cell methods. The advantages of these methods include good long time behaviors and constraints preservation, which are validated by numerical experiments