An SPQR-tree of a biconnected planar graph G represents a recursive decomposition of G with respect to its split pairs. It can be used to represent all planarembeddings of G. First I will give a short introduction to SPQR-trees and andshow how to construct them. Then I will demonstrate how this data-structure canbe used to represent all embeddings of a graph. In the second half of the talk,I will introduce an integer linear program that is based on the decomposition represented by the SPQR-tree with the property that the set of solutions represents exactly the set of all planar embeddings of the graph.