Understanding the structure of the cost landscape of optimisation problems is important for algorithm design. In this talk, I discuss one approach based on Barrier Trees which captures the structure of the local minima and barriers between minima for search spaces with up to 10^12 states. This structure allows visualisation of heuristic search strategies. Furthermore, the visualisation can be used to construct a model of the problem which captures many of the relevant features of the real problem, but with a vastly reduced number of states. The model can be used for investigating optimal heuristic strategies.