  Gibbs measures are the main object of study in equilibrium statistical
mechanics, and are used in many other contexts, including dynamical systems and
ergodic theory, and spatial statistics. However, in a large number of natural
instances one encounters measures that are not of Gibbsian form. We present
here a number of examples of such non-Gibbsian measures, and discuss some of
the underlying mathematical and physical issues to which they gave rise.
