Low-quality face recognition (LQFR) has received increasing attention over the past few years. There are numerous potential uses for systems with LQFR capability in real-world environments when high-resolution or high-quality images are difficult or impossible to capture. One of the significant potential application domains for LQFR systems is video surveillance. As the number of surveillance cameras increases (especially in urban environments), the videos that they capture will need to be processed automatically. However, those videos are usually captured with large standoffs, challenging illumination conditions, and diverse angles of view. Faces in these images are generally small in size. Past work on this topic has employed techniques such as super-resolution processing, deblurring, or learning a relationship between different resolution domains. In this paper, we provide a comprehensive review of approaches to low-quality face recognition in the past six years. First, a general problem definition is given, followed by a systematic analysis of the works on this topic by category. Next, we highlight the relevant data sets and summarize their respective experimental results. Finally, we discuss the general limitations and propose priorities for future research.