  The languages generated by interval exchange transformations have been
characterized by Ferenczi-Zamboni (2008) and Belov-Cernyatev (2010) under some
extra conditions on the system. Lifting these conditions leads us to consider
successively natural codings of standard interval exchange transformations,
natural codings of affine interval exchange transformations, grouped codings of
affine interval exchange transformations, and natural codings of generalized
interval exchange transformations. We show that these four classes of languages
are strictly increasing, and give necessary and/or sufficient (but not all
equally explicit) combinatorial criteria to describe each of them. These work
also, mutatis mutandis, for interval exchanges with flips
