  Local symmetries is one of the most successful themes in modern theoretical
physics. Although they are usually associated to Lie algebras, a gradual
increase of interest in more general situations where local symmetries are
associated to groupoids and algebroids has taken place in recent years. On the
other hand, dualities is another persistently interesting theme in modern
physics. One of the most prominent examples is provided by target space duality
in string theory. The latter, Abelian or not, is usually associated to the
presence of isometries, which is however a very restrictive assumption. In this
contribution we discuss some recent advances located at the intersection of the
above two themes. Focusing on bosonic string sigma models we discuss certain
gauged versions where (a) the invariance conditions on the background fields
are much milder than the isometric case and (b) the gauge symmetry is
generically associated to a Lie algebroid instead of just a Lie algebra.
Furthermore we utilize such gauged sigma models to study the possibility of
non-Abelian, non-isometric T-duality.
