In 1980 the anomalous sub-barrier fusion of two massive atomic nuclei was discovered. In this review we examine the experimental findings that the cross sections for subbarrier fusion far exceed simple quantum tunnelling expectations, and the magnitude of the excess fusion is particularly sensitive to the valence structure of the collision partners. The phenomenon is interpreted as one which occurs when intrinsic degrees of freedom of the dinuclear system couple to the tunnelling degree of freedom. Several models, developed during the period from 1983-5, serve to illustrate the salient features of coupling-aided barrier penetration. We discuss the nature of the couplings and the underlying dynamics, focusing our attention on the quasi-elastic channels (inelastic scattering and nucleon transfer). Results of studies on quasi-elastic scattering and of the fusion partial-wave distributions, completed during the past three years, are then presented.