Protein kinases are involved in regulating diverse and essential cellular processes, and their dysfunction is implicated in many diseases, making them key drug targets. Crystallographic and NMR studies, as well as computational simulations, have shown that kinases are inherently dynamic and flexible molecules, interconverting spontaneously between active and inactive conformations, often via high-energy transitional states. Here, we use a recent theoretical method based on graph theory -- Markov Stability -- to analyse the multiscale structural organisation and dynamics of kinases, and to predict the effects of mutations, post-translational modifications and protein--protein interactions. Results are presented for the Src-family and related kinases, for which we corroborate known activating mutations associated with cancer and make additional predictions to be tested experimentally. Another major focus of this work is the family of cyclin-dependent kinases (cdks), key regulators of the mammalian cell cycle which are potential therapeutic targets for cancer. The cdks are highly conserved in sequence and structure, especially in their active sites, and it has traditionally been difficult to explain the differences in function between them. Our results include predictions for potential loss-of-function mutations and allosteric binding sites, as well as dynamic information that may be relevant to currently unanswered questions such as the loss of function of the analogue-sensitive cdk2 mutant. Additionally, we assess the level of confidence we have in our results and its dependence on noise and error in the underlying data using a newly developed quantitative method for comparing clusterings on different graphs, and investigate the `resolution limit' of the method by amending the methodology to accommodate very-low-resolution structures.