We review some of the recent results on two-interacting particles (TIP) in
low-dimensional disordered quantum models. Special attention is given to th
e mapping of the problem onto random band matrices. In particular, we const
ruct two simple, seemingly closely related examples for which an analogous
mapping leads to incorrect results. We briefly discuss possible reasons for
this discrepancy based on the physical differences between the TIP problem
and our examples. (C) 2001 Elsevier Science B.V. All rights reserved.