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As communities represent similar opinions, similar functions, similar purposes, etc., community detection is an important and extremely useful tool in both scientific inquiry and data analytics. However, the classic methods of community detection, such as spectral clustering and statistical inference, are falling by the wayside as deep learning techniques demonstrate an increasing capacity to handle high-dimensional graph data with impressive performance. Thus, a survey of current progress in community detection through deep learning is timely. Structured into three broad research streams in this domain - deep neural networks, deep graph embedding, and graph neural networks, this article summarizes the contributions of the various frameworks, models, and algorithms in each stream along with the current challenges that remain unsolved and the future research opportunities yet to be explored.