Periocular refers to the facial region in the vicinity of the eye, including eyelids, lashes and eyebrows. While face and irises have been extensively studied, the periocular region has emerged as a promising trait for unconstrained biometrics, following demands for increased robustness of face or iris systems. With a surprisingly high discrimination ability, this region can be easily obtained with existing setups for face and iris, and the requirement of user cooperation can be relaxed, thus facilitating the interaction with biometric systems. It is also available over a wide range of distances even when the iris texture cannot be reliably obtained (low resolution) or under partial face occlusion (close distances). Here, we review the state of the art in periocular biometrics research. A number of aspects are described, including: i) existing databases, ii) algorithms for periocular detection and/or segmentation, iii) features employed for recognition, iv) identification of the most discriminative regions of the periocular area, v) comparison with iris and face modalities, vi) soft-biometrics (gender/ethnicity classification), and vii) impact of gender transformation and plastic surgery on the recognition accuracy. This work is expected to provide an insight of the most relevant issues in periocular biometrics, giving a comprehensive coverage of the existing literature and current state of the art.