  After the introduction of $\lambda$-symmetries by Muriel and Romero, several
other types of so called "twisted symmetries" have been considered in the
literature (their name refers to the fact they are defined through a
deformation of the familiar prolongation operation); they are as useful as
standard symmetries for what concerns symmetry reduction of ODEs or
determination of special (invariant) solutions for PDEs and have thus attracted
attention. The geometrical relation of twisted symmetries to standard ones has
already been noted: for some type of twisted symmetries (in particular,
$\lambda$ and $\mu$-symmetries), this amounts to a certain kind of gauge
transformation.
  In a previous review paper [G. Gaeta, "Twisted symmetries of differential
equations", {\it J. Nonlin. Math. Phys.}, {\bf 16-S} (2009), 107-136] we have
surveyed the first part of the developments of this theory; in the present
paper we review recent developments. In particular, we provide a unifying
geometrical description of the different types of twisted symmetries; this is
based on the classical Frobenius reduction applied to distribution generated by
Lie-point (local) symmetries.
