Atmospheric science relies on numerical models to simulate the complex, multiscale nature of atmospheric variability, but our confidence in weather and climate predictions relies on theory and simplified models that describe scale interactions at a mechanistic level and can provide causal accounts of atmospheric behaviour. Global simulations at kilometre-scale resolution are now feasible and offer new opportunities to the atmospheric science community for testing and expanding our understanding of climate variability and change. Taking full advantage of this new tool requires smart strategies for evaluating and analysing the output, especially as kilometre-scale climate modelling will be limited to relatively short simulations with a rather small number of realizations. We here review some of the available tools for diagnosing and studying the dynamics of waves, coherent flows, and the interactions between them in terms of their ability to provide causal accounts of the behaviour seen in observations and in comprehensive simulation models. We describe their successes but also some of their limitations. The limitations are seen to be especially pronounced in the tropics, where clouds, convection and atmospheric circulation are inextricably linked. The lack of a natural spatial truncation scale in the tropics has given rise to many theoretical challenges, but it is for precisely this reason that the tropics are where we might expect the largest gain from global kilometre-scale models.