Abstract Recent developments in the dynamical microscopic theories of cluster decay are reviewed with special emphasis on the nuclear structure aspects and physical interpretation of the models. What we call dynamical microscopic theories are those in which the decay width is derived from the nucleonic structures, of the participating nuclei, which are deduced through the solution of their equations of motion. After a brief review of the various expressions for the decay width, we turn to the nuclear-structure aspects of the problem. We thoroughly discuss the treatment of the Pauli effects in models involving macroscopic elements. We settle the long-standing controversy over the cluster-core norm operator that relates microscopic and macroscopic relative-motion wave functions in the transition amplitude. We conclude that the way the norm operator was originally introduced in the mid-1970s is in principle correct. The main part of the paper is a detailed review, in which the approaches considered are categorized according to the structure models used for the parent nucleus. The approaches discussed are the ordinary shell models, the cluster-like shell models and the Bardeen-Cooper-Schrieffer (BCS) approach. By discussing these diverse calculations, it is concluded that the most essential prerequisite for a realistic model of the mother nucleus is that it should correctly describe the cluster correlation in the surface region. This implies that the proton-neutron interaction is indispensable, and the moderate success of ordinary shell models is accounted for by their failure to include both proton-neutron interaction and large enough bases. For the special case of a doubly-closed-shell residual state, cluster-like models are able to cope with this problem, because their bases are more economical, and, for these cases, they provide a fully satisfactory decay theory. The BCS approach, on the other hand, is widely applicable, and is the only one that has been applied to heavy-cluster decay with reasonable success. We point out, however, that the formation amplitude calculated in this model still contains approximations. We explain the success of the BCS theory by showing that, in spite of appearance, it does include proton-neutron interaction, in an effective manner. In discussing the results for the widths, we address the problem of the preformation probability of a cluster-core pair in the parent nucleus. One can be fairly confident that in the ground state of 212Po the amount of core-α-clustering is as high as 20–30%, but, in respect of other cluster-decaying nuclei, the theory is not yet conclusive. We conclude that a satisfactory understanding of heavy-cluster radioactivity requires the application of both more sophisticated cluster models and improved BCS approaches.