The problem of turbulence is the greatest unsolved problem of classical physics. It is encountered in dynamical systems so complicated that numerical calculations are too expensive. In practice it is often suffcient to know only a few time-averaged quantities, such as the mean drag and lift. The problem of turbulence is the problem of establishing methods of obtaining this limited information at a significantly smaller cost than the cost of getting the complete solution. Even finding good upper and lower bounds for the quantity of interest might be enough. The talk will cover the basics of how this can be done, then move on to new developments related to the recent advances in computer-assisted semi-algebraic optimisation, and finish with unsolved problems.