  Discrete arrays of Josephson junction elements differ from their continuum
counterparts in two essential ways: i) localized dynamic states in discrete
arrays, which are not present in the corresponding continuum system, can
interact with other excitations that are present; ii) fluxoid quantization for
the non-superconducting `holes' provides a constraint for discrete arrays that
is not present in the corresponding continuum system. The consequences of these
effects in one-dimensional systems are now beginning to be understood; in
two-dimesional systems, on the other hand, the picture is not yet altogether
clear. Progress in fabrication technology and potential applications in
practical electronic devices -- as well as intrinsic interest in nonlinear
dynamics -- have contributed significantly to the growing interest in these
systems.
