Nowadays, digital cameras and smart phones play an increasingly important role in daily lives, and have become the main tools for people to perceive the world, record information and communicate with each other. When these devices are used to shoot electronic screens, the irregular Moiré patterns in the image are produced due to the overlap of the display devices and digital grids of the camera sensor, which seriously affects the visual quality of the captured images. Therefore, the removal of Moiré pattern is of great significance for the post-processing of captured images. In this paper, recent research about Moiré removal is reviewed in detail, and the existing methods are classified into two categories according to different application scenarios and technical implementations: prior knowledge based Moiré removal and deep learning based methods respectively. According to different training data acquisition and alignment approaches, deep learning based Moiré removal techniques can be divided into convolutional neural network (CNN) based methods and generative adversarial network (GAN) based methods. Then, based on the same public dataset, we implement the mainstream deep learning based Moiré removal algorithms, compare and analyze their performance, and summarize the advantages and disadvantages of various methods. Finally, discuss possible directions for future research.