  This paper is a survey of some of the developments in coarse extrinsic
geometry since its inception in the work of Gromov. Distortion, as measured by
comparing the diameter of balls relative to different metrics, can be regarded
as one of the simplist extrinsic notions. Results and examples concerning
distorted subgroups, especially in the context of hyperbolic groups and
symmetric spaces, are exposed. Other topics considered are quasiconvexity of
subgroups; behaviour at infinity, or more precisely continuous extensions of
embedding maps to Gromov boundaries in the context of hyperbolic groups acting
by isometries on hyperbolic metric spaces; and distortion as measured using
various other filling invariants.
