A graph is one of the most general data structures in computer science. For example, a graph can model connected atoms in molecules, linked web pages, computer networks, befriended people in social networks, neighboring pixels, and graphical symbols in document images, to name just a few. In graph-based pattern recognition, the availability of efficient methods for graph comparison is crucial. Typical challenges include problems with high computational complexity and the question how to integrate machine learning into the matching process. To tackle these challenges, we investigate efficient approximations of graph edit distance and geometric deep learning methods, among others.