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Graph Neural Networks (GNNs) have shown superb performance in handling networked data, mainly attributed to their message passing and convolution process across neighbors. For most literature, the performance of GNNs is mainly reported based on noise-free data environments. No study has systematically evaluated GNNs’ performance under noise. In this article, we carry out an empirical study and theoretical analysis of four types of GNNs, including Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Contrastive Networks (GCL), and graph UniFilter under three types of noise, including attribute noise, structure noise, and label noise. Our study shows that GNNs behave tremendously differently in response to different types of noise. Overall, GAT is the most noise vulnerable and sensitive, whereas GCL is the most noise resilient. We further carry out theoretical analysis to explain the reason causing GAT to be sensitive to noise, and propose a solution to enhance its noise resilience. Our study brings in-depth firsthand knowledge of GNNs under noise for researchers and practitioners to better utilize GNNs in real-world applications.