ThisConvex lifting chapter presents the latest developments in convex lifting, a powerful tool belonging to the class of lift-and-project techniques with various applications in control systems design. According to the active research on the topic, this technique demonstrates its capability in convexifying arduous problems, such as the constrained controllerController design, fragilityFragility analysis of piecewise affine controllers, or pathPath planningPath planning in cluttered environments. The advantages are various and span from memory reduction and efficientEfficient online evaluationEvaluation for piecewise affine controllers to the reformulation of recedingHorizon horizon control into bilevel optimization. Still, they can also extend to the sensitivity of piecewise affine control laws for linear discrete-time systems with state and input constraints. On the latter topic, the impact of perturbations on state-spaceSpace partitions is shown to be efficiently evaluated and can lead to a region-free PWA controlPWA control using induced fragilityFragility margins. The present chapter recalls all these trends and completes the presentation with the extension of convex liftings for the path generation for staticStatic congested multi-obstacleObstacle environments, thus simplifying pathPath selection and the generation of feasibleFeasible navigation corridors.