  In this paper we address several new developments in the theory of dc
Josephson effect in superconducting weak links. We analyze an interplay between
quantum interference effects and Andreev reflection in SNS nanojunctions with
insulating barriers and demonstrate that such effects may qualitatively modify
the Josephson current in such structures. We also investigate an impact of the
parity effect on persistent currents in superconducting nanorings interrupted
by a quantum point contact (QPC). In the limit of zero temperature and for the
odd number of electrons in the ring we predict complete suppression of the
supercurrent across QPC with one conducting mode. In nanorings with SNS
junctions a $\pi$-state can occur for the odd number of electrons. Changing
this number from even to odd yields spontaneous supercurrent in the ground
state of such rings without any externally applied magnetic flux.
