  The generalized Dehn twist along a closed curve in an oriented surface is an
algebraic construction which involves intersections of loops in the surface. It
is defined as an automorphism of the Malcev completion of the fundamental group
of the surface. As the name suggests, for the case where the curve has no
self-intersection, it is induced from the usual Dehn twist along the curve. In
this expository article, after explaining their definition, we review several
results about generalized Dehn twists such as their realizability as
diffeomorphisms of the surface, their diagrammatic description in terms of
decorated trees and the Hopf-algebraic framework underlying their construction.
Going to the dimension three, we also overview the relation between generalized
Dehn twists and $3$-dimensional homology cobordisms, and we survey the variants
of generalized Dehn twists for skein algebras of the surface.
