In this talk, we focus on finite element methods for the delayed nonlinear reaction-diffusion system with smooth and non-smooth solutions, by using finite difference methods (including uniform and nonuniform schemes) in time. The optimal convergence and superconvergence results are derived. Moreover, in order to improve computational efficiency, fast algorithms are built for the above proposed numerical schemes based on the sum-of-exponentials (SOE) approximation. Finally, some numerical experiments are provided to confirm the theoretical analysis and show the effectiveness of the fast algorithms.