It is well known that in the computational fluid dynamics simulations related to the cardiovascular system the enforcement of outflow boundary conditions is a crucial point. In fact, they highly affect the computed flow and a wrong setup could lead to unphysical results. In this chapter we discuss the main features of two different ways for the estimation of proper outlet boundary conditions in the context of hemodynamics simulations: on one side, a lumped parameter model of the downstream circulation and, on the other one, a technique based on optimal control.