This paper outlines modern optimal control theory and its possible application to the design of some aircraft control systems. Both continuous and discrete control laws are considered. Deterministic linear systems with a quadratic index of performance (state feedback) are discussed and extended to real and implicit model-following. Output feedback control laws are introduced using gain matrices and state observers, leading to the (Stochastic) Kalman-Bucy filter. The effects of plant parameter variation with flight condition are related to the design of ‘desensitised’ control laws. Comment is also made on suitable state variable models.