In this paper, we consider the face swapping detection from the perspective of face identity. Face swapping aims to replace the target face with the source face and generate the fake face that the human cannot distinguish between real and fake. We argue that the fake face contains the explicit identity and implicit identity, which respectively corresponds to the identity of the source face and target face during face swapping. Note that the explicit identities of faces can be extracted by regular face recognizers. Particularly, the implicit identity of real face is consistent with the its explicit identity. Thus the difference between explicit and implicit identity of face facilitates face swapping detection. Following this idea, we propose a novel implicit identity driven framework for face swapping detection. Specifically, we design an explicit identity contrast (EIC) loss and an implicit identity exploration (IIE) loss, which supervises a CNN backbone to embed face images into the implicit identity space. Under the guidance of EIC, real samples are pulled closer to their explicit identities, while fake samples are pushed away from their explicit identities. Moreover, IIE is derived from the margin-based classification loss function, which encourages the fake faces with known target identities to enjoy intra-class compactness and inter-class diversity. Extensive experiments and visualizations on several datasets demonstrate the generalization of our method against the state-of-the-art counterparts.