  We give an equivalent characterisation for the existence of a semi-conjugacy
to an irrational rotation for conservative homeomorphisms of the two-torus.
This leads to an analogue of Poincare's classification of circle homeomorphisms
for conservative toral homeomorphisms with unique rotation vector and a certain
bounded mean motion property. For minimal toral homeomorphisms, the result
extends to arbitrary dimensions. Further, we provide a basic classification for
the dynamics of non-wandering toral homeomorphisms homotopic to the identitiy.
