  Various properties of mesoscopic two-dimensional Josephson junction arrays
are reviewed. Particular attention is paid to structure of the topological
excitations, charges and vortices, which are shown to be dual to each other.
This duality persists in the presence of external magnetic fields and offset
charges, which influence vortices and charges in an equivalent way. A
double-layer junction array is also considered, where an even further reaching
duality is discovered.
