  We present a concise, but systematic, review of the ergodicity issue in
strongly correlated systems. After giving a brief historical overview, we
analyze the issue within the Green's function formalism by means of the
equations of motion approach. By means of this analysis, we are able to
individuate the primary source of non-ergodic dynamics for a generic operator
and also to give a recipe to compute unknown quantities characterizing such a
behavior within the Composite Operator Method. Finally, we present examples of
non-trivial strongly correlated systems where it is possible to find a
non-ergodic behavior.

Strongly Correlated Electrons;Soft Condensed Matter