  We review recent progress in applying information- and computation-theoretic
measures to describe material structure that transcends previous methods based
on exact geometric symmetries. We discuss the necessary theoretical background
for this new toolset and show how the new techniques detect and describe novel
material properties. We discuss how the approach relates to well known
crystallographic practice and examine how it provides novel interpretations of
familiar structures. Throughout, we concentrate on disordered materials that,
while important, have received less attention both theoretically and
experimentally than those with either periodic or aperiodic order.
