The purpose of this paper is to examine the problem of controlling a linear time-invariant system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semiglobal framework for this problem is a natural one. Within this framework, a set of solvability conditions are given and feedback laws that solve the problem are constructed. The theory developed in this paper incorporates earlier results established for linear systems without input saturation.