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Graph Neural Networks (GNNs) have exploded onto themachine learning scene in recent years owing to their capability to model and learn from graph-structured data. Such an ability has strong implications in a wide variety of ields whose data are inherently relational, for which conventional neural networks do not perform well. Indeed, as recent reviews can attest, research in the area of GNNs has grown rapidly and has lead to the development of a variety of GNN algorithm variants as well as to the exploration of ground-breaking applications in chemistry, neurology, electronics, or communication networks, among others. At the current stage research, however, the eicient processing of GNNs is still an open challenge for several reasons. Besides of their novelty, GNNs are hard to compute due to their dependence on the input graph, their combination of dense and very sparse operations, or the need to scale to huge graphs in some applications. In this context, this article aims to make two main contributions. On the one hand, a review of the ield of GNNs is presented from the perspective of computing. This includes a brief tutorial on the GNN fundamentals, an overview of the evolution of the ield in the last decade, and a summary of operations carried out in the multiple phases of diferent GNN algorithm variants. On the other hand, an in-depth analysis of current software and hardware acceleration schemes is provided, fromwhich a hardware-software, graph-aware, and communication-centric vision for GNN accelerators is distilled. [ABSTRACT FROM AUTHOR]