Super-resolution is the problem of generating one or a set of high-resolution images from one or a sequence of low-resolution frames. Most methods have been proposed for super-resolution based on multiple low resolution images of the same scene, which is called multiple-frame super-resolution. Only a few approaches produce a high-resolution image from a single low-resolution image, with the help of one or a set of training images from scenes of the same or different types. It is referred to as single-frame super-resolution. This article reviews a variety of single-frame super-resolution methods proposed in the recent years. In the paper, a new manifold learning method: locally linear embedding (LLE) and its relation with single-frame super-resolution is introduced. Detailed study of a critical issue: "neighborhood issue" is presented with related experimental results and analysis and possible future research is given.