  The goal of this paper is to give an exposition of some results of
Bestvina-Mess on local connectivity of the boundary of a one-ended word
hyperbolic group. We also give elementary proofs that all hyperbolic groups are
semistable at infinity and their boundaries are linearly connected in the
one-ended case. Geoghegan first observed that semistability at infinity is a
consequence of local connectivity using ideas from shape theory, and
Bonk-Kleiner proved linear connectivity using analytical methods. The methods
in this paper are closely based on the original ideas of Bestvina-Mess.
