Limitations of current adjoint-based optimisation algorithms when applied to turbulent flows motivated work on the Least Square Shadowing method, that produces reliable sensitivities of time-averaged quantities to variations of system parameters. We have developed a highly efficient algorithm that makes the convergence rate of the Shadowing method almost independent of the size of the dynamical system and the length of the trajectory used to compute the time-average. Very recently, we applied shadowing for feedback control of chaotic systems. We have also coupled it with polynomial chaos expansion for uncertainty quantification of time-average quantities and their sensitivities when the system parameters follow a prescribed probability density function. This coupling resulted in a faster approach, named Shadowed Polynomial Chaos Expansion.