  Darboux transformations for linear operators on regular two dimensional
lattices are reviewed. The six point scheme is considered as the master linear
problem, whose various specifications, reductions, and their sublattice
combinations lead to other linear operators together with the corresponding
Darboux transformations. The second part of the review deals with
multidimensional aspects of (basic reductions of) the four point scheme, as
well as the three point scheme.
