A new facet of image restoration research has begun to emerge in recent years: super-resolution of images, which we define as the processing of an image so as to recover object information from beyond the spatial frequency bandwidth of the optical system that formed the image. Simple Fourier analysis would indicate that super-resolution is not possible. Therefore, it is important to reconcile this simplistic view with the existing algorithms that have been demonstrated to achieve super-resolution. In this article, we consider some of the algorithms that have demonstrated super-resolution and discuss the common principles that they share which makes it possible for them to recover some of the lost bandwidth of the object. We also consider the question of super-resolution performance, which is the measure of how much lost bandwidth can be recovered from a super-resolution algorithm, and how the performance is related to the algorithm principles that allow super-resolution to occur. We conclude with examples of super-resolution.