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Image reconstruction from undersampled k-space data has been playing an important role in fast magnetic resonance imaging (MRI). Recently, deep learning has demonstrated tremendous success in various fields and also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of deep-learning-based image reconstruction methods for MRI. Two types of deep-learningbased approaches are reviewed, those that are based on unrolled algorithms and those that are not, and the main structures of both are explained. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed, which may facilitate further development of the networks and performance analysis from a theoretical point of view.