  Dimer models are a combinatorial tool to describe certain algebras that
appear as noncommutative crepant resolutions of toric Gorenstein singularities.
Unfortunately, not every dimer model gives rise to a noncommutative crepant
resolution. Several notions of consistency have been introduced to deal with
this problem. In this paper we study the major different notions in detail and
show that for dimer models on a torus they are all equivalent.
