Inverse halftoning is an ill-posed problem that refers to the problem of restoring continuous-tone images from their halftone versions. Although much progress has been achieved over the last decades, the restored images still suffer from detail loss and visual artifacts. Recent studies show that inverse halftoning methods based on deep learning are superior to other traditional methods, and thus this paper aimed to systematically review the inverse halftone methods based on deep learning, so as to provide a reference for the development of inverse halftoning. In this paper, we firstly proposed a classification method for inverse halftoning methods on the basis of the source of halftone images. Then, two types of inverse halftoning methods for digital halftone images and scanned halftone images were investigated in terms of network architecture, loss functions, and training strategies. Furthermore, we studied existing image quality evaluation including subjective and objective evaluation by experiments. The evaluation results demonstrated that methods based on multiple subnetworks and methods based on multi-stage strategies are superior to other methods. In addition, the perceptual loss and the gradient loss are helpful for improving the quality of restored images. Finally, we gave the future research directions by analyzing the shortcomings of existing inverse halftoning methods.