  Knots and links which are closed 3-braids are a very special class. Like
2-bridge knots and links, they are simple enough to admit a complete
classification. At the same time they are rich enough to serve as a source of
examples on which, with luck, a researcher may be able to test various
conjectures. The goal of this review article is to gather together, in one
place, some of the tools that are special to knots and links of braid index 3,
in a form that could be useful for those who have a need to calculate, and need
to know precisely all the exceptional cases. We also use it as an opportunity
to review what is known and suggest some open questions.
