Image super-resolution reconstruction is an image processing technology, which recovers high-resolution images from low-resolution images. While, the super-resolution problem is under-determined. In recent years, researchers have proposed learning-based methods to learn image prior information from a large amount of data, in order to constrain the super-resolution solution space. This paper introduces the mainstream image super-resolution reconstruction algorithms in the past two decades, which are divided into two categories: traditional features based methods and deep learning based methods. For the traditional super-resolution reconstruction algorithms, this paper mainly presents the methods based on neighborhood embedding, the methods based on sparse representation, and the methods based on local linear regression. For the deep learning based methods, the super-resolution model design, the up-sampling method and the loss function form are provided. In addition, this paper introduces the application of super-resolution reconstruction technology in video super-resolution, remote-sensing image super-resolution, and high-level vision tasks. Finally, the future development directions of image super-resolution reconstruction technology are provided.