  This document is built around a list of thirty-two problems in enumeration of
matchings, the first twenty of which were presented in a lecture at MSRI in the
fall of 1996. I begin with a capsule history of the topic of enumeration of
matchings. The twenty original problems, with commentary, comprise the bulk of
the article. I give an account of the progress that has been made on these
problems as of this writing, and include pointers to both the printed and
on-line literature; roughly half of the original twenty problems were solved by
participants in the MSRI Workshop on Combinatorics, their students, and others,
between 1996 and 1999. The article concludes with a dozen new open problems.
(Note: This article supersedes math.CO/9801060 and math.CO/9801061.)
