Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs -- sets of elements and their pairwise relations -- and are a central method within the broader field of geometric deep learning. They are very expressive and have demonstrated superior performance to other classical deep learning approaches in a variety of domains. The data in particle physics are often represented by sets and graphs and as such, graph neural networks offer key advantages. Here we review various applications of graph neural networks in particle physics, including different graph constructions, model architectures and learning objectives, as well as key open problems in particle physics for which graph neural networks are promising.