Satellite imageries are an important geoinformation source for different applications in the Earth Science field. However, due to the limitation of the optic and sensor technologies and the high cost to update the sensors and equipments, the spectral and spatial resolution of the Earth Observation satellites may not meet the desired requirements. Thus, Remote Sensing Image Super-resolution (RSISR) which aims at restoring the high-resolution (HR) remote sensing images from the given low-resolution (LR) images has drawn considerable attention and witnessed the rapid development of the deep learning (DL) algorithms. In this research, we aim to compre-hensively review the DL-based single image super-resolution (SISR) methods on optical remote sensing images. First, we introduce the DL techniques utilized in SISR. Second, we summarize the RSISR algorithms thoroughly, including the DL models, commonly used remote sensing datasets, loss functions, and performance evaluation metrics. Third, we present a new multi-sensor dataset that consists of Very High-Resolution satellite images from different satellites of various landscapes and evaluate the performance of some state-of-the-art super-resolution methods on this dataset. Finally, we envision the challenges and future research in the RSISR field.