While simulation methods in the field of Computational Fluid Dynamics (CFD) are already quite advanced,
efficient and well developed numerical approaches for optimisation and optimal control in CFD are still
under development. Particular challenges in this context are optimisation problems with instationary flows,
resulting in discrete nonlinear systems of equations with an extremely high number of unknowns. We give a
short overview about current developments in the field of solvers for such situations. Our emphasis will be
placed on special space-time multigrid based solution strategies which are able to solve the underlying
nonlinear system of equations with linear complexity.