Moiré pattern in a single image is common in image visual quality degradation induced by frequency aliasing between cameras and monitors when taking a screen-shot photo. It is mainly resulted from the interference between the pixel grids of the camera sensor and the device screen. However, removal of the Moiré patterns is challenging based on the complex frequency distribution and imbalanced magnitude in color channels. Only a few studies in the literature focused on the solution of Moiré pattern removal from a single image. Traditional studies usually treated the problem as an image denoising problem and applied some filtering or signal decomposition operations based on some image priors (e.g., sparsity). Relying on the rapid development of the deep learning techniques, some deep learning-based approaches of Moiré pattern removal have been presented recently. This paper presents a brief survey and comparative study for the recent deep learning-based research works on Moiré pattern removal and discusses possible further research directions.