Graph Neural Networks (GNNs) have emerged as powerful representation learning tools for capturing complex dependencies within diverse graph-structured data. Despite their success in a wide range of graph mining tasks, GNNs have raised serious concerns regarding their trustworthiness, including susceptibility to distribution shift, biases towards certain populations, and lack of explainability. Recently, integrating causal learning techniques into GNNs has sparked numerous ground-breaking studies since many GNN trustworthiness issues can be alleviated by capturing the underlying data causality rather than superficial correlations. In this survey, we comprehensively review recent research efforts on Causality-Inspired GNNs (CIGNNs). Specifically, we first employ causal tools to analyze the primary trustworthiness risks of existing GNNs, underscoring the necessity for GNNs to comprehend the causal mechanisms within graph data. Moreover, we introduce a taxonomy of CIGNNs based on the type of causal learning capability they are equipped with, i.e., causal reasoning and causal representation learning. Besides, we systematically introduce typical methods within each category and discuss how they mitigate trustworthiness risks. Finally, we summarize useful resources and discuss several future directions, hoping to shed light on new research opportunities in this emerging field. The representative papers, along with open-source data and codes, are available in https://github.com/usail-hkust/Causality-Inspired-GNNs.
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