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This paper comprehensively surveys the development of face hallucination (FH), including both face super-resolution and face sketch-photo synthesis techniques. Indeed, these two techniques share the same objective of inferring a target face image (e.g. high-resolution face image, face sketch and face photo) from a corresponding source input (e.g. low-resolution face image, face photo and face sketch). Considering the critical role of image interpretation in modern intelligent systems for authentication, surveillance, law enforcement, security control, and entertainment, FH has attracted growing attention in recent years. Existing FH methods can be grouped into four categories: Bayesian inference approaches, subspace learning approaches, a combination of Bayesian inference and subspace learning approaches, and sparse representation-based approaches. In spite of achieving a certain level of development, FH is limited in its success by complex application conditions such as variant illuminations, poses, or views. This paper provides a holistic understanding and deep insight into FH, and presents a comparative analysis of representative methods and promising future directions.