Deep face recognition (FR) has achieved significantly high accuracy on several challenging datasets and fosters successful real-world applications, even showing high robustness to the illumination variation that is usually regarded as a main threat to the FR system. However, in the real world, illumination variation caused by diverse lighting conditions cannot be fully covered by the limited face dataset. In this paper, we study the threat of lighting against FR from a new angle, i.e., adversarial attack, and identify a new task, i.e., adversarial relighting. Given a face image, adversarial relighting aims to produce a naturally relighted counterpart while fooling the state-of-the-art deep FR methods. To this end, we first propose the physical model-based adversarial relighting attack (ARA) denoted as albedo-quotient-based adversarial relighting attack (AQ-ARA). It generates natural adversarial light under the physical lighting model and guidance of FR systems and synthesizes adversarially relighted face images. Moreover, we propose the auto-predictive adversarial relighting attack (AP-ARA) by training an adversarial relighting network (ARNet) to automatically predict the adversarial light in a one-step manner according to different input faces, allowing efficiency-sensitive applications. More importantly, we propose to transfer the above digital attacks to physical ARA (Phy-ARA) through a precise relighting device, making the estimated adversarial lighting condition reproducible in the real world. We validate our methods on three state-of-the-art deep FR methods, i.e., FaceNet, ArcFace, and CosFace, on two public datasets. The extensive and insightful results demonstrate our work can generate realistic adversarial relighted face images fooling FR easily, revealing the threat of specific light directions and strengths.