DeepFake detection has so far been dominated by ``artifact-driven methods and the detection performance significantly degrades when either the type of image artifacts is unknown or the artifacts are simply too hard to find. In this work, we present an alternative approach: Identity-Driven DeepFake Detection. Our approach takes as input the suspect image/video as well as the target identity information (a reference image or video). We output a decision on whether the identity in the suspect image/video is the same as the target identity. Our motivation is to prevent the most common and harmful DeepFakes that spread false information of a targeted person. The identity-based approach is fundamentally different in that it does not attempt to detect image artifacts. Instead, it focuses on whether the identity in the suspect image/video is true. To facilitate research on identity-based detection, we present a new large scale dataset ``Vox-DeepFake, in which each suspect content is associated with multiple reference images collected from videos of a target identity. We also present a simple identity-based detection algorithm called the OuterFace, which may serve as a baseline for further research. Even trained without fake videos, the OuterFace algorithm achieves superior detection accuracy and generalizes well to different DeepFake methods, and is robust with respect to video degradation techniques -- a performance not achievable with existing detection algorithms.