The lack of resolution of imaging systems has critically adverse impacts on the recognition and performance of biometric systems, especially in the case of long range biometrics and surveillance such as face recognition at a distance, iris recognition and gait recognition . Super-resolution, as one of the core innovations in computer vision , has been an attractive but challenging solution to address this problem in both general imaging systems and biometric systems. However, a fundamental difference exists between conventional super-resolution motivations and those required for biometrics. The former aims to enhance the visual clarity of the scene while the latter, more significantly, aims to improve the recognition accuracy of classifiers by exploiting specific characteristics of the observed biometric traits . This paper comprehensively surveys the state-of-the-art super-resolution approaches proposed for four major biometric modalities: face (2D+3D), iris, fingerprint and gait. We approach the super-resolution problem in biometrics from several different perspectives, including from the spatial and frequency domains, single and multiple input images, learning-based and reconstruction-based approaches. Especially, we highlight two special categories: feature-domain super-resolution which performs super-resolution directly on the feature space to purposely improve the recognition performance, and deep-learning super-resolution which discusses the most recent advances in deep learning for the super-resolution task. Finally, we discuss the current and open research challenges and provide recommendations into the future for the improved use of super-resolution with biometrics.