Graph matching plays a key role in many areas of computing from computer vision to networks where there is a need to determine correspondences between the components (vertices and edges) of two attributed structures. In recent years three new approaches to graph matching have emerged as replacements to more traditional heuristic methods. These new methods are: * Least squares - where the optimal correspondence in determined in terms of deriving the best fitting permutation matrix between sets. * Spectral methods - where optimal correspondences are derived via subspace projections in the graph eigenspaces. * Graphical models - where algorithms such as the junction tree algorithm are used to infer the optimal labeling of the nodes of one graph in terms of the other and that satisfy similarity constraints between vertices and edges. In this lecture we review and compare these methods and demonstrate examples where this applies to point set and line matching.