  This survey reviews Kauffman's model of folded ribbon knots: knots made of a
thin strip of paper folded flat in the plane. The ribbonlength is the length to
width ratio of such a ribbon, and the ribbonlength problem asks to minimize the
ribbonlength for a given knot type. We give a summary of known results. For the
most part, these are upper bounds of ribbonlength of twist knots and certain
families of torus knots. We discuss result of G. Tian, which give upper bounds
of ribbonlength in terms of crossing number. In addition, it turns out the
choice of fold affects the ribbonlength. We end with a discussion of three
different types of folded ribbon equivalence and give examples illustrating
their relationship to ribbonlength.
