In this talk, we first construct an arbitrarily high order energy stable scheme for solving the nonlocal Cahn-Hilliard equation based on IEQ approach and the Runge-Kutta method. We prove that the proposed scheme is unconditional energy stable and can preserve the energy dissipation law. Then, by using the idea of SAV and “zero-energy-contribution” approach, a highly efficient fully-decoupled, linear, second-order and unconditionally energy stable scheme for the nonlocal two-phase incompressible flows is developed. At each time step, we only needs to solve a few poisson-type equations with constant coefficients. The unconditional energy stability of the scheme is proved. Finally, some numerical simulations in 2D and 3D are carried out to demonstrate the accuracy, stability, and effectiveness of the scheme.