  This paper is a survey about the Thurston metric on the Teichm\"uller space.
The central issue is the constructions of extremal Lipschitz maps between
hyperbolic surfaces. We review several constructions, including the original
work of Thurston. Coarse geometry and isometry rigidity of the Thurston metric,
relation between the Thurston metric and the Thurston compactification are
discussed. Some recent generalizations and developments of the Thurston metric
are sketched.
