Summary. -Microscopic calculations of cluster decay widths, which have been one of the recurrent challenges of nuclear theory for many years, require a good description of the preformed cluster in the mother nucleus. Since the cluster being emitted is formed either at the nuclear surface or beyond it, a reasonable microscopic description of the clustering requires the use of a realistic finite single-particle potential, including its continuum. In this paper, recent developments in the dynamical theories of cluster decay are reviewed with special emphasis on the influence of the continuum in the decay process.The ordinary shell models, including the BCS approach, are discussed. Also clusterlike shell model theories, which incorporate the most important effects of the continuum, are presented.By discussing 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 as well as the clustering at large distances. This implies, on the one side, that the proton-neutron interaction is indispensable and, on the other, that high-lying configurations, reflecting the influence of the continuum, have to be taken into account properly.I will mainly present the work that I have done in collaboration with a number of researchers, as shown in the list of references. For a recent and detailed review of this work see ref.[1], from which much of the material to be presented here is taken.The formation and decay of clusters in nuclei is a time-dependent problem. It is therefore a very difficult problem, particularly because the initial state is not well defined. One