In this talk, we will introduce some results about the initial boundary value problems for compressible Navier-Stokes-Poisson equations on exterior domains. With the radial symmetry assumption, the global existence of solutions to compressible Navier-Stokes-Poisson equations with the large initial data on a domain exterior to a ball in R^n(n ≥1) is proved. Moreover, without any symmetry assumption, the global existence of smooth solutions near a given constant steady state for compressible Navier-Stokes-Poisson equations on an exterior domain in R^3 with physical boundary conditions is also established with the exponential stability. Furthermore, an initial boundary value problem for compressible Magnetohydrodynamics (MHD) is considered on an exterior domain (with the first Betti number vanishes) in R^3. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established.