This review is devoted to the control problem with constraints on the magnitude and rate of change of the control action in aircraft control systems. In engineering practice, it is accepted to use actuators with a sufficiently large level of magnitude and energy supply. Theoretical investigations in the field of systems with saturation in the control loop should provide engineers with design methods for the minimization (as much as possible) of the weight–size and energy characteristics of actuators. Therefore, such investigations are highly relevant for practice. The review is focused on a specific effect that can occur when there is an integral component in the control law, the so-called integrator windup, that leads to the deterioration of the quality of system processes, a significant increase in control errors, sometimes to the loss of function associated with the occurrence of large amplitude limit cycles, and even to a loss of stability. The occurrence of this effect in aircraft flights can have dramatic consequences. Thus, the suppression of this effect is an urgent task for designing aircraft control systems. The main part of this review is devoted to the corresponding methods.