The control system of a nuclear reactor is an important distributed parameter system governed by the neutron transport equation. This paper summarizes part of the authors and their colleagues' recent work on this subject, including the spectral analysis of the neutron transport operator, the asymptotic stability theory of the solution of the time dependent transport equation, the convergence of the discrete-ordinate method for the time dependent neutron transport equation, the optimal control and identification problems arising from the nuclear reactor, etc.