  The exchange graph of a cluster algebra encodes the combinatorics of
mutations of clusters. Through the recent "categorifications" of cluster
algebras using representation theory one obtains a whole variety of exchange
graphs associated with objects such as a finite-dimensional algebra or a
differential graded algebra concentrated in non-positive degrees. These
constructions often come from variations of the concept of tilting, the
vertices of the exchange graph being torsion pairs, t-structures, silting
objects, support $\tau$-tilting modules and so on. All these exchange graphs
stemming from representation theory have the additional feature that they are
the Hasse quiver of a partial order which is naturally defined for the objects.
In this sense, the exchange graphs studied in this article can be considered as
a generalization or as a completion of the poset of tilting modules which has
been studied by Happel and Unger. The goal of this article is to axiomatize the
thus obtained structure of an ordered exchange graph, to present the various
constructions of ordered exchange graphs and to relate them among each other.
