Deep learning-based models have been very successful in achieving state-of-the-art results in many of the computer vision, speech recognition, and natural language processing tasks in the last few years. These models seem a natural fit for handling the everincreasing scale of biometric recognition problems, from cellphone authentication to airport security systems. Deep learning-based models have increasingly been leveraged to improve the accuracy of different biometric recognition systems in recent years. In this work, we provide a comprehensive survey of more than 120 promising works on biometric recognition (including face, fingerprint, iris, palmprint, ear, voice, signature, and gait recognition), which deploy deep learning models, and show their strengths and potentials in different applications. For each biometric, we first introduce the available datasets that are widely used in the literature and their characteristics. We will then talk about several promising deep learning works developed for that biometric, and show their performance on popular public benchmarks. We will also discuss some of the main challenges while using these models for biometric recognition, and possible future directions to which research in this area is headed.