In this talk, we present some works on two Vlasov systems. One is the classical Vlasov-Poisson-Boltzmann system that has been well studied. With the understanding on its spectrum structure, we prove the diffusion limit of the unipolar VPB system to the incompressible Navier-Stokes-Fourier system in the perturbative framework. The second model to be considered is the Vlasov-Nordstrom-Fokker-Planck system for which we show the stability of the Maxwell-Juttner distribution with constant scalar gravitational field. The first study is a joint work with Hailiang Li and Mingying Zhong and the second one is a joint work with Renjun Duan and Shuangqian Liu.