  We propose several common extensions of the classes of Anosov subgroups and
geometrically finite Kleinian groups among discrete subgroups of semisimple Lie
groups. We relativize various dynamical and coarse geometric characterizations
of Anosov subgroups given in our earlier work, extending the class from
intrinsically hyperbolic to relatively hyperbolic subgroups. We prove
implications and equivalences between the various relativizations.
