In this paper we consider the two seemingly disparate areas of linear input constrained Model Predictive Control (MPC) and Antiwindup control as frameworks to deal with actuator saturations. The MPC framework gives rise to a quadratic program whose solution satisfies the Karush-Kuhn-Tucker (KKT) conditions. Here we demonstrate that these KKT conditions form a set of implicit equations that may be represented as a block diagram containing an algebraic loop. Furthermore, this block diagram can be formed as a direct extension of antiwindup compensation. We also briefly discuss state constraint versions of the results as well as extended antiwindup type structures which exploit sparsity. The key overall result is that linear input constrained MPC is (globally) equivalent to antiwindup extended to include prediction of future control actions, their saturations, and compensation based on this.