  Graph Neural Networks (GNNs), neural network architectures targeted to
learning representations of graphs, have become a popular learning model for
prediction tasks on nodes, graphs and configurations of points, with wide
success in practice. This article summarizes a selection of the emerging
theoretical results on approximation and learning properties of widely used
message passing GNNs and higher-order GNNs, focusing on representation,
generalization and extrapolation. Along the way, it summarizes mathematical
connections.
