This thesis is focused on the design of advanced suspension systems (active and semi-active) using time-domain optimal control methods. This work has been strongly motivated by the need to develop an approach to active and semi-active suspensions which was ready to be applied directly in a prototype vehicle, and which would have the potential to be deployed in production. We develop a general design framework for time-domain optimal control of active suspensions that aims to treat both the ride quality (response to road disturbances) and handling (response to driver inputs) in combination. The handling inputs can be approximated by external forces on the vehicle body and they can represent inertial loads induced by manoeuvres, aerodynamical forces as well as changes to static loads. The aspect of handling performance is often ignored in the optimal control literature for vehicle suspensions. We show that ignoring the handling aspect in the controller design can lead to performance degradation such as state estimation deterioration in the case of incomplete measurements. We generalise the performance criterion to a risk-sensitive exponential LQG criterion. In this way, the control-power matrix in the Riccati equation will be altered so that the designer can potentially have a direct influence on ride performance. For the optimal control of semi-active suspensions two performance criteria are considered. The necessary conditions for optimality for the first criterion are shown to be satisfied by bang-bang and singular controls. A full characterisation of the switchings on intervals of bang-bang controls is presented as well as a discussion on the optimality of singular controls. For the second performance criterion an optimal control for the finite horizon and a suboptimal stationary control are given. A conjecture that the semi-active clipped-optimal control gives lower cost than the optimal fixed passive damper, for all admissible initial conditions, is presented. An application of an LQ optimal control to a realistic nonlinear vehicle model for active and semiactive actuators is carried out and a comparison with a fixed passive system for realistic road profiles and handling manoeuvres is presented. The experimental testing on a prototype vehicle of the semi-active control algorithm developed in this thesis is described. The state estimation with the proposed observer is found to be satisfactory during handling manoeuvres, whereas ignoring the load disturbances in the observer design causes estimation degradation. A comparison with a fixed passive suspension is presented.