In this talk, we discuss the asymptotic behavior of solutions to a Navier-Stokes model when the external force contains hereditary characteristics (constant, distributed or variable delay, memory, etc). First we prove the existence and uniqueness of solutions by Galerkin approximations and the energy method. Next, the existence of stationary solution is established by Lax-Milgram theorem and Schauder fixed point theorem. Then the local stability analysis of stationary solution is studied by using the theory of Lyapunov functions and the Razumikhin-Lyapunov technique. In the end, Lyapunov functionals is also exploited to obtain some stability results.