  Self-distributive (SD) structures form an important class of solutions to the
Yang--Baxter equation, which underlie spectacular knot-theoretic applications
of self-distributivity. It is less known that one go the other way round, and
construct an SD structure out of any left non-degenerate (LND) set-theoretic
YBE solution. This structure captures important properties of the solution:
invertibility, involutivity, biquandle-ness, the associated braid group
actions. Surprisingly, the tools used to study these associated SD structures
also apply to the cohomology of LND solutions, which generalizes SD cohomology.
Namely, they yield an explicit isomorphism between two cohomology theories for
these solutions, which until recently were studied independently. The whole
story leaves numerous open questions. One of them is the relation between the
cohomologies of a YBE solution and its associated SD structure. These and
related questions are covered in the present survey.
