My proposal centers around materials where the atoms are organised in a crystal structure. Many macroscopic properties of such materials are determined by the collective behaviour of the electrons in the outer orbitals of the atoms. These electrons can either be mobile and move between atoms, or be frozen in place in which case there can still be interesting interactions between the spins of the different electrons. Depending on how these electrons behave, the material can for example be an insulator, conductor, paramagnet, ferro-magnet or antiferromagnet. These types of materials can all be understood using band theory or the Landau-Ginzburg-Wilson (LGW) theory of symmetry breaking. However, in recent years it has become clear that at low temperatures there exists a variety of different insulators and paramagnets, each with their own distinct universal physical properties. These materials correspond to truly different phases of matter, which can not be explained using the LGW paradigm. In this proposal I address the question of how to identify such phases, either in numerical simulations or via experimentally detectable properties. For symmetry-breaking phases in the LGW theory one numerically identifies the phase by calculating order parameters, which is not possible for the more unconventional phases. Rapid development of experimental techniques also poses many questions on how one would realise these new materials and measure the defining physical properties.