The key objective of super-resolution (SR) imaging is to reconstruct a higher-resolution image based on a set of images, acquired from the same scene and denoted as ‘low-resolution’ images, to overcome the limitation and/or ill-posed conditions of the image acquisition process for facilitating better content visualization and scene recognition. In this paper, we provide a comprehensive review of SR image and video reconstruction methods developed in the literature and highlight the future research challenges. The SR image approaches reconstruct a single higher-resolution image from a set of given lower-resolution images, and the SR video approaches reconstruct an image sequence with a higher-resolution from a group of adjacent lower-resolution image frames. Furthermore, several SR applications are discussed to contribute some insightful comments on future SR research directions. Specifically, the SR computations for multi-view images and the SR video computation in the temporal domain are discussed.