Due to the limitations of imaging mechanisms, the current technical conditions of remote sensing hardware are not yet able to acquire multi-band remote sensing images with high spatial and high spectral resolution simultaneously. Multi-band remote sensing image is a three-dimensional image collection that reflects the information of different narrow-band intervals. It contains two-dimensional spatial information and one-dimensional spectral information. The spatial information reflects the geometric characteristics of the scene, and the spectral information corresponds to the electromagnetic wave characteristics of the ground objects in different bands. To compensate for the deficiency of spatial information acquisition in multi-band remote sensing images, sharpening of the images, which enhances their spatial resolution by using auxiliary images, has been emphasized. The sharpening of multi-band remote sensing images can not only improve the visual effect of the images, but also lay the foundation for subsequent qualitative and quantitative remote sensing applications such as ground object classification, change detection and parameter inversion, and thus has been a very significant and continuously active research direction in the field of remote sensing image processing. This paper reviews the research progress of multi-band remote sensing image sharpening methods. Firstly, the connotation of multi-band remote sensing image sharpening is expressed. Secondly, from the perspective of panchromatic sharpening of multispectral (MS) images and in the context of algorithm implementation techniques, the research progress and problems of MS image sharpening methods based on Component Substitution (CS), Multi-resolution Analysis (MRA), Optimization Model (OM) and Deep Learning (DL) are investigated and discussed respectively. Thirdly, the sharpening characteristics of HS images are analyzed in light of the characteristics of Hyperspectral (HS) images that are different from those of MS, and some specific HS sharpening methods that are different from those of MS are discussed and summarized. Finally, the future development of multi-band remote sensing image sharpening methods is prospected. The reasons why the CS and MRA methods are currently more recognized by the mainstream and the future sharpening field will show a relevant convergence of multiple methods are discussed, respectively.