Abstract: With the fast development and wide application of remote sensing technology, remote sensing images with higher quality are needed. However, it is difficult to directly acquire high-resolution, multispectral remote sensing images. To obtain high-quality images by integrating the information from different imaging sensors, pansharpening technology emerged. Pansharpening is an effective method used to obtain multispectral images with high spatial resolution. Many scholars have studied this method and obtained fruitful achievements. In recent years, deep learning theory has developed rapidly and has been widely applied in pansharpening. This study aims to systematically introduce the progress in pansharpening and promote its development. To this end, this study first introduced the traditional, classical pansharpening methods, followed by commonly used remote sensing satellites. Then, this study elaborated on the pansharpening methods based on deep learning from the perspective of supervised learning, unsupervised learning, and semi-supervised learning. After that, it described and analyzed loss functions. To demonstrate the superiority of the pansharpening methods based on deep learning and analyze the effects of loss functions, this study conducted remote sensing image fusion experiments. Finally, this study presented the future prospects of the pansharpening methods based on deep learning.