Josephson effects in quantum microstructures

This paper is written to commemorate the 50th anniversary of the discovery of the Josephson effect. A review is presented of recent theoretical research on the Josephson effect in several kinds of quantum microstructures, including the fundamental physical phenomenon of the Josephson effect and its peculiar features in various new materials, such as the 0-π transition in graphene nanoribbons, the chiral edge supercurrents in two-dimensional topological insulators, and the Josephson effect and DC-AC current transition between exciton polariton condensates in semiconductor microcavities.