Deep Convolutional Neural Networks (DCNNs) have become the state-of-the-art computational models of biological object recognition. Their remarkable success has helped vision science break new ground. Consequently, recent efforts have started to transfer this achievement to the domain of biological face recognition. In this regard, face detection can be investigated through comparisons of face-selective biological areas and neurons to artificial layers and units. Similarly, face identification can be examined through comparisons of in vivo and in silico face space representations. In this mini-review, we summarize the first studies with this aim. We argue that DCNNs are useful models, which follow the general hierarchical organization of biological face recognition. In two spotlights, we emphasize unique scientific contributions of these models. Firstly, studies on face detection in DCNNs propose that elementary face-selectivity emerges automatically through feedforward processes. Secondly, studies on face identification in DCNNs suggest that experience and additional generative mechanisms are required for this challenge. Taken together, as this novel computational approach enables close control of predisposition (i.e., architecture) and experience (i.e., training data), this could also inform longstanding debates on the substrates of biological face recognition.