A technique of quasi-optimum control was developed by the author in 1966. The goal of the technique was to permit one to use the apparatus of optimum control theory without having to solve the two-point boundary value problem for the actual problem. This was achieved by assuming the actual problem is "near" a simplified problem the solution of which was known. In this case, the control law adds a linear correction to the costate of the simplified problem. The linear correction is obtained as the solution of a matrix Riccati equation. During the 1960s and early 1970s the efficacy of the technique was demonstrated in by several guidance and control examples. With the resurgence of interest in optimum control via the Hamilton-Jacobi-Bellman equation, it is timely to revisit the quasi-optimum control technique. After a review of the theory, several new examples are provided to illustrate how the technique can be applied. These include mildly nonlinear processes, processes with bounded-control, and processes with state-variable constraints. After a discussion of alternate suboptimal control techniques, the paper concludes with a discussion of some issues remaining with the method.