The dynamics of superstring, supergravity and M-theories and their compactifications are probed by studying the various perturbation theories that emerge in the strong and weak-coupling limits for various directions in coupling constant space. The results support the picture of an underlying non-perturbative theory that, when expanded perturbatively in different coupling constants, gives different perturbation theories, which can be perturbative superstring theories or superparticle theories. The p-brane spectrum is considered in detail and a criterion found to establish which p-branes govern the strong-coupling dynamics. In many cases there are competing conjectures in the literature, and this analysis decides between them. In other cases, new results are found. The chiral 6-dimensional theory resulting from compactifying the type IIB string on K3 is studied in detail and it is found that certain strong-coupling limits appear to give new theories, some of which hint at the possibility of a 12-dimensional origin.