Although many interesting phenomena have been understood, the field is still very active. One of the most difficult problems is the problem of localization in the presence of an electron-electron interactions. Study of disordered systems with a direction described by effective non-Hermitian Hamiltonians is one more topic attracting a considerable interest. The latter approach is sure to be a powerful method of study disordered systems without interaction. Extending this method to the case of interacting systems is a big challenge for a future work.
Computational methods can be also of great help in understanding different aspects.
One more topic is study of critical behavior near phase transitions in the presence of disorder. As an example, critical behavior of the Ising model with long-range disorder is studied at present. Researchers in the group are trying to understand these unusual aspects of criticality. By now it is well established that energy spectra of quantum counterparts of classically chaotic finite systems obey Wigner-Dyson level statistics. This understanding came initially through numerous computer simulations and semiclassical considerations.