  We review our recent results on Anderson localization in systems of two
interacting particles coupled by contact interactions. Based on an exact
mapping to an effective single-particle problem, we numerically investigate the
occurrence of metal-insulator phase transitions for the pair in two- (2D) and
three-dimensional (3D) disordered lattices. In two dimensions, we find that
interactions cause an exponential enhancement of the pair localization length
with respect to its single-particle counterpart, but do not induce a
delocalization transition. In particular we show that previous claims of 2D
interaction-induced Anderson transitions are the results of strong finite-size
effects. In three dimensions we find that the pair undergoes a metal-insulator
transition belonging to the same (orthogonal) universality class of the
noninteracting model. We then explore the phase diagram in the space of energy
E, disorder W and interaction strength U, which reveals a rich and
counterintuitive structure, endowed with multiple metallic and insulating
phases. We point out that this phenomenon originates from the molecular and
scattering-like nature of the pair states available at given energy and
disorder strength.
