Distribution shifts on graphs -- the data distribution discrepancies between training and testing a graph machine learning model, are often ubiquitous and unavoidable in real-world scenarios. Such shifts may severely deteriorate the performance of the model, posing significant challenges for reliable graph machine learning. Consequently, there has been a surge in research on graph Out-Of-Distribution (OOD) adaptation methods that aim to mitigate the distribution shifts and adapt the knowledge from one distribution to another. In our survey, we provide an up-to-date and forward-looking review of graph OOD adaptation methods, covering two main problem scenarios including training-time as well as test-time graph OOD adaptation. We start by formally formulating the two problems and then discuss different types of distribution shifts on graphs. Based on our proposed taxonomy for graph OOD adaptation, we systematically categorize the existing methods according to their learning paradigm and investigate the techniques behind them. Finally, we point out promising research directions and the corresponding challenges. We also provide a continuously updated reading list at https://github.com/kaize0409/Awesome-Graph-OOD-Adaptation.git
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