Ordered structures arise naturally in many problems and proofs in discrete geometry. For example, the unit distance problem for convex polygons stimulated the extremal theory of 0–1 matrices. Similarly, the study of point-set configurations, known as the study of order types, plays an important role in geometric problems such as rectilinear crossing numbers and the happy ending problem.

In extremal, probabilistic, and structural combinatorics, many objects and arguments possess natural orderings. For example, the Erdős–Hajnal stepping-up argument for hypergraph Ramsey numbers processes vertices one by one according to a fixed order. Similarly, the resolution of the Stanley–Wilf conjecture relies on 0–1 matrices, which may be viewed loosely as ordered analogues of bipartite graphs.