  This paper describes the use of simple lattice models for studying the
properties of structurally disordered systems like glasses and granulates. The
models considered have crystalline states as ground states, finite
connectivity, and are not subject to constrained evolution rules. After a short
review of some of these models, the paper discusses how two particularly simple
kinds of models, the Potts model and the exclusion models, evolve after a
quench at low temperature to glassy states rather than to crystalline states.
