  The exact solution of the BCS pairing Hamiltonian was found by Richardson in
1963. While little attention was paid to this exactly solvable model in the
remainder of the 20th century, there was a burst of work at the beginning of
this century focusing on its applications in different areas of quantum
physics. We review the history of this exact solution and discuss recent
developments related to the Richardson-Gaudin class of integrable models,
focussing on the role of these various models in nuclear physics.
