In this paper, we present an effective and efficient face deblurring algorithm by exploiting semantic cues via deep convolutional neural networks (CNNs). As face images are highly structured and share several key semantic components (e.g., eyes and mouths), the semantic information of a face provides a strong prior for restoration. As such, we propose to incorporate global semantic priors as input and impose local structure losses to regularize the output within a multi-scale deep CNN. We train the network with perceptual and adversarial losses to generate photo-realistic results and develop an incremental training strategy to handle random blur kernels in the wild. Quantitative and qualitative evaluations demonstrate that the proposed face deblurring algorithm restores sharp images with more facial details and performs favorably against state-of-the-art methods in terms of restoration quality, face recognition and execution speed.