  Spatial aperiodicity occurs in various models and material s. Although today
the most well-known examples occur in the area of quasicrystals, other
applications might also be of interest. Here we discuss some issues related to
the notion and occurrence of aperiodic order in equilibrium statistical
mechanics. In particular, we consider some spectral characterisations,and
shortly review what is known about the occurrence of aperiodic order in lattice
models at zero and non-zero temperatures. At the end some more speculative
connections to the theory of (spin-)glasses are indicated.
