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Machine learning plays an increasingly important role in many areas of chemistry and materials science, e.g. to predict materials properties, to accelerate simulations, to design new materials, and to predict synthesis routes of new materials. Graph neural networks (GNNs) are one of the fastest growing classes of machine learning models. They are of particular relevance for chemistry and materials science, as they directly work on a graph or structural representation of molecules and materials and therefore have full access to all relevant information required to characterize materials. In this review article, we provide an overview of the basic principles of GNNs, widely used datasets, and state-of-the-art architectures, followed by a discussion of a wide range of recent applications of GNNs in chemistry and materials science, and concluding with a road-map for the further development and application of GNNs.