In almost every physical application, the actuator has bounds on its input, and thus actuator saturation is important to study. Also, it is quite possible that the system becomes unstable when input saturation constraints are considered. In this chapter, we consider the global consensus problem for discrete-time networked dynamical systems with input saturation constraints under fixed undirected graphs. We first give necessary conditions for achieving the global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents. We then focus on two special cases, where the agent dynamics are either neutrally stable or double integrator. For the neutrally stable case, any linear protocol of a particular form, which solves the consensus problem for the case without input saturation constraints, also solves the global consensus problem for the case with input saturation constraints. For the double integrator case, we show that a subset of linear protocols, which solve the consensus problem for the case without input saturation constraints, also solve the global consensus problem for the case with input saturation constraints. The results are illustrated by numerical simulations.