  The Turaev cobracket, a loop operation introduced by V. Turaev, which
measures self-intersection of a loop on a surface, is a modification of a path
operation introduced earlier by Turaev himself, as well as a counterpart of the
Goldman bracket. In this survey based on the author's joint works with A.
Alekseev, Y. Kuno and F. Naef, we review some algebraic aspects of the
cobracket and its framed variants including their formal description, an
application to the mapping class group of the surface and a relation to the
(higher genus) Kashiwara-Vergne problem. In addition, we review a homological
description of the cobracket after R. Hain.
