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Magnetic resonance imaging is a powerful imaging modality that can provide versatile information. However, it has a fundamental challenge that is time consuming to acquire images with high quality and high resolution. Reducing the scanned measurements can significantly accelerate its speed with the aid of the powerful reconstruction methods, which has evolved from linear analytic reconstructions to nonlinear iterative ones. The emerging trend in this area is replacing human-defined signal models with that learned from data. Specifically, from 2016, deep learning has been incorporated into the fast MR imaging task, which draws valuable prior knowledge from big datasets to facilitate accurate MR image reconstruction from limited measurements. Many researchers believed this started a new era of fast MR imaging techniques, namely learning reconstruction. This survey aims to review the main works in …