  The Douglas--Rachford method is a splitting method frequently employed for
finding zeroes of sums of maximally monotone operators. When the operators in
question are normal cones operators, the iterated process may be used to solve
feasibility problems of the form: Find $x \in \bigcap_{k=1}^N S_k.$ The success
of the method in the context of closed, convex, nonempty sets $S_1,\dots,S_N$
is well-known and understood from a theoretical standpoint. However, its
performance in the nonconvex context is less understood yet surprisingly
impressive. This was particularly compelling to Jonathan M. Borwein who,
intrigued by Elser, Rankenburg, and Thibault's success in applying the method
for solving Sudoku Puzzles, began an investigation of his own. We survey the
current body of literature on the subject, and we summarize its history. We
especially commemorate Professor Borwein's celebrated contributions to the
area.
