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In recent years, researchers have proposed many deep learning (DL) methods for various tasks, and particularly face recognition (FR) made an enormous leap using these techniques. Deep FR systems benefit from the hierarchical architecture of the DL methods to learn discriminative face representation. Therefore, DL techniques significantly improve state-of-the-art performance on FR systems and encourage diverse and efficient real-world applications. In this paper, we present a comprehensive analysis of various FR systems that leverage the different types of DL techniques, and for the study, we summarize 171 recent contributions from this area. We discuss the papers related to different algorithms, architectures, loss functions, activation functions, datasets, challenges, improvement ideas, current and future trends of DL-based FR systems. We provide a detailed discussion of various DL methods to understand the current state-of-the-art, and then we discuss various activation and loss functions for the methods. Additionally, we summarize different datasets used widely for FR tasks and discuss challenges related to illumination, expression, pose variations, and occlusion. Finally, we discuss improvement ideas, current and future trends of FR tasks.