  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
