Recently proposed robust 3D face alignment methods establish either dense or sparse correspondence between a 3D face model and a 2D facial image. The use of these methods presents new challenges as well as opportunities for facial texture analysis. In particular, by sampling the image using the fitted model, a facial UV can be created. Unfortunately, due to self-occlusion, such a UV map is always incomplete. In this paper, we propose a framework for training Deep Convolutional Neural Network (DCNN) to complete the facial UV map extracted from in-the-wild images. To this end, we first gather complete UV maps by fitting a 3D Morphable Model (3DMM) to various multiview image and video datasets, as well as leveraging on a new 3D dataset with over 3,000 identities. Second, we devise a meticulously designed architecture that combines local and global adversarial DCNNs to learn an identity-preserving facial UV completion model. We demonstrate that by attaching the completed UV to the fitted mesh and generating instances of arbitrary poses, we can increase pose variations for training deep face recognition/verification models, and minimise pose discrepancy during testing, which lead to better performance. Experiments on both controlled and in-the-wild UV datasets prove the effectiveness of our adversarial UV completion model. We achieve state-of-the-art verification accuracy, 94.05%, under the CFP frontal-profile protocol only by combining pose augmentation during training and pose discrepancy reduction during testing. We will release the first in-the-wild UV dataset (we refer as WildUV) that comprises of complete facial UV maps from 1,892 identities for research purposes.