A pseudolinear drawing of a graph is one in which the edges can be extended to an arrangement of pseudolines. Arrangements of pseudolines are a useful tool for tackling many problems in Discrete Geometry (and the Crossing Number Problem is not the exception). The Crossing Number Problem is to find the minimum number of crossings in any drawing of a given graph.

In this talk, I will present a characterization of the pseudolinear drawings of graphs (a joint work with Julien Bensmail and Bruce Richter). Then, I will show how this characterization provides a framework for studying crossing numbers.