A drawing of a finite graph is convex if its vertices can be represented as points in the plane in convex position, and its edges as straight-line segments joining these points.
In this talk we present some results about the minimum number of crossings among convex drawings of arbitrary graphs. In particular, we will show an enhanced version of the so called “Crossing Lemma” for convex drawings. This is joint work with Silvia Fernández-Merchant.