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At present, with the advance of satellite image processing technology, remote sensing images are becoming more widely used in real scenes. However, due to the limitations of current remote sensing imaging technology and the influence of the external environment, the resolution of remote sensing images often struggles to meet application requirements. In order to obtain high-resolution remote sensing images, image super-resolution methods are gradually being applied to the recovery and reconstruction of remote sensing images. The use of image super-resolution methods can overcome the current limitations of remote sensing image acquisition systems and acquisition environments, solving the problems of poor-quality remote sensing images, blurred regions of interest, and the requirement for high-efficiency image reconstruction, a research topic that is of significant relevance to image processing. In recent years, there has been tremendous progress made in image super-resolution methods, driven by the continuous development of deep learning algorithms. In this paper, we provide a comprehensive overview and analysis of deep-learning-based image super-resolution methods. Specifically, we first introduce the research background and details of image super-resolution techniques. Second, we present some important works on remote sensing image super-resolution, such as training and testing datasets, image quality and model performance evaluation methods, model design principles, related applications, etc. Finally, we point out some existing problems and future directions in the field of remote sensing image super-resolution. [ABSTRACT FROM AUTHOR]