  The use of exactly-solvable Richardson-Gaudin (R-G) models to describe the
physics of systems with strong pair correlations is reviewed. We begin with a
brief discussion of Richardson's early work, which demonstrated the exact
solvability of the pure pairing model, and then show how that work has evolved
recently into a much richer class of exactly-solvable models. We then show how
the Richardson solution leads naturally to an exact analogy between such
quantum models and classical electrostatic problems in two dimensions. This is
then used to demonstrate formally how BCS theory emerges as the large-N limit
of the pure pairing Hamiltonian and is followed by several applications to
problems of relevance to condensed matter physics, nuclear physics and the
physics of confined systems. Some of the interesting effects that are discussed
in the context of these exactly-solvable models include: (1) the crossover from
superconductivity to a fluctuation-dominated regime in small metallic grains,
(2) the role of the nucleon Pauli principle in suppressing the effects of high
spin bosons in interacting boson models of nuclei, and (3) the possibility of
fragmentation in confined boson systems. Interesting insight is also provided
into the origin of the superconducting phase transition both in two-dimensional
electronic systems and in atomic nuclei, based on the electrostatic image of
the corresponding exactly-solvable quantum pairing models.
