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Speaker recognition is a task of identifying persons from their voices. Recently, deep learning has dramatically revolutionized speaker recognition. However, there is lack of comprehensive reviews on the exciting progress. In this paper, we review several major subtasks of speaker recognition, including speaker verification, identification, diarization, and robust speaker recognition, with a focus on deep-learning-based methods. Because the major advantage of deep learning over conventional methods is its representation ability, which is able to produce highly abstract embedding features from utterances, we first pay close attention to deep-learning-based speaker feature extraction, including the inputs, network structures, temporal pooling strategies, and objective functions respectively, which are the fundamental components of many speaker recognition subtasks. Then, we make an overview of speaker diarization, with an emphasis of recent supervised, end-to-end, and online diarization. Finally, we survey robust speaker recognition from the perspectives of domain adaptation and speech enhancement, which are two major approaches of dealing with domain mismatch and noise problems. Popular and recently released corpora are listed at the end of the paper.