Face super-resolution, also known as face hallucination, which is aimed at enhancing the resolution of low-resolution (LR) one or a sequence of face images to generate the corresponding high-resolution (HR) face images, is a domain-specific image super-resolution problem. Recently, face super-resolution has received considerable attention, and witnessed dazzling advances with deep learning techniques. To date, few summaries of the studies on the deep learning-based face super-resolution are available. In this survey, we present a comprehensive review of deep learning techniques in face super-resolution in a systematic manner. First, we summarize the problem formulation of face super-resolution. Second, we compare the differences between generic image super-resolution and face super-resolution. Third, datasets and performance metrics commonly used in facial hallucination are presented. Fourth, we roughly categorize existing methods according to the utilization of face-specific information. In