Automatic face recognition is an area with immense practical potential which includes a wide range of commercial and law enforcement applications. Hence it is unsurprising that it continues to be one of the most active research areas of computer vision. Even after over three decades of intense research, the state-of-the-art in face recognition continues to improve, benefitting from advances in a range of different research fields such as image processing, pattern recognition, computer graphics, and physiology. Systems based on visible spectrum images, the most researched face recognition modality, have reached a significant level of maturity with some practical success. However, they continue to face challenges in the presence of illumination, pose and expression changes, as well as facial disguises, all of which can significantly decrease recognition accuracy. Amongst various approaches which have been proposed in an attempt to overcome these limitations, the use of infrared (IR) imaging has emerged as a particularly promising research direction. This paper presents a comprehensive and timely review of the literature on this subject. Our key contributions are (i) a summary of the inherent properties of infrared imaging which makes this modality promising in the context of face recognition; (ii) a systematic review of the most influential approaches, with a focus on emerging common trends as well as key differences between alternative methodologies; (iii) a description of the main databases of infrared facial images available to the researcher; and lastly (iv) a discussion of the most promising avenues for future research.