The capacity to recognize faces under varied poses is a fundamental human ability that presents a unique challenge for computer vision systems. Compared to frontal face recognition, which has been intensively studied and has gradually matured in the past few decades, pose-invariant face recognition (PIFR) remains a largely unsolved problem. However, PIFR is crucial to realizing the full potential of face recognition for real-world applications, since face recognition is intrinsically a passive biometric technology for recognizing uncooperative subjects. In this paper, we discuss the inherent difficulties in PIFR and present a comprehensive review of established techniques. Existing PIFR methods can be grouped into four categories, i.e., pose-robust feature extraction approaches, multi-view subspace learning approaches, face synthesis approaches, and hybrid approaches. The motivations, strategies, pros/cons, and performance of representative approaches are described and compared. Moreover, promising directions for future research are discussed.