Recent studies show that convolutional neural networks (CNNs) are vulnerable under various settings, including adversarial attacks, common corruptions, and backdoor attacks. Motivated by the findings that human visual sys-tem pays more attention to global structure (e.g., shapes) for recognition while CNNs are biased towards local texture features in images, in this work we aim to analyze whether "edge features" could improve the recognition robustness in these scenarios, and if so, to what extent? To answer these questions and systematically evaluate the global structure features, we focus on shape features and pro-pose two edge-enabled pipelines EdgeNetRob and Edge-GANRob, forcing the CNNs to rely more on edge features. Specifically, EdgeNetRob and EdgeGANRob first explicitly extract shape structure features from a given image via an edge detection algorithm. Then EdgeNetRob trains down-stream learning tasks directly on the extracted edge features, while EdgeGANRob reconstructs a new image by refilling the texture information with a trained generative adversarial network (GANs). To reduce the sensitivity of edge detection algorithms to perturbations, we additionally propose a robust edge detection approach Robust Canny based on vanilla Canny. Based on our evaluation, we find that EdgeNetRob can help boost model robustness under different attack scenarios at the cost of the clean model accuracy. EdgeGANRob, on the other hand, is able to improve the clean model accuracy compared to EdgeNetRob while preserving the robustness. This shows that given such edge features, how to leverage them matters for robustness, and it also depends on data properties. Our systematic studies on edge structure features under different settings will shed light on future robust feature exploration and optimization.