In this talk, we discuss the validity of Hilbert expansion for the relativistic Vlasov-Maxwell-Boltzmann system. The global-in-time validity of its Hilbert expansion is established and the limiting relativistic Euler-Maxwell system is derived as the mean free path goes to zero. Our method is based on an extended $L^2-L^{\infty}$ framework and the Glassey-Strauss Representation of the electromagnetic field.