  The advent of radioactive ion beam facilities and new detector technologies
have opened up new possibilities to investigate the radioactive decays of
highly unstable nuclei, in particular the proton emission, $\alpha$ decay and
heavy cluster decays from neutron-deficient (or proton-rich) nuclei around the
proton drip line. It turns out that these decay measurements can serve as a
unique probe for studying the structure of the nuclei involved. On the
theoretical side, the development in nuclear many-body theories and
supercomputing facilities have also made it possible to simulate the nuclear
clusterization and decays from a microscopic and consistent perspective. In
this article we would like to review the current status of these structure and
decay studies in heavy nuclei, regarding both experimental and theoretical
opportunities. We then discuss in detail the recent progress in our
understanding of the nuclear $\alpha$ formation probabilities in heavy nuclei
and their indication on the underlying nuclear structure.
