Abstract: We present a short survey of the following set of extremal problems. Let $t$ be a type of a non-crossing graph (such as a triangulation, a non-crossing spanning tree, a non-crossing perfect matching, etc.). Let $N_t$ be the maximal number of graphs of type $t$ that can be drawn on a fixed set of $n$ points in the plane. We wish to find the asymptotic value of $N_t$. For example, what is the maximal number of non-crossing spanning trees for a set of $n$ points in the plane. Research on such problems have led to the development of some important tools in combinatorial geometry and in general combinatorics. These include the Catalan numbers and the crossing lemma. In this presentation, we will not focus on a specific result or on a specific problem, but rather present several interesting results and proofs that this sub(-sub-sub)-field has generated.