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

On the prevalence of non-Gibbsian states in mathematical physics