With the development of stereo imaging technology, stereo image super-resolution has attracted increasing attention in recent years. Different from single image super-resolution, stereo image super-resolution can further improve the quality of image reconstruction by using the complementary information between left and right view images. In this paper, we present a comprehensive survey on recent advances of stereo image super-resolution field. Firstly, we introduce the fundamental theory of stereo imaging. Then, we review the existing stereo image super-resolution algorithms and stereo image datasets. Afterwards, we comprehensively evaluate several mainstream deep learning-based stereo image super-resolution algorithms on benchmark datasets, and investigate the influences of different training sets on the performances of super-resolution algorithms. Finally, we summarize challenges and prospect future research directions in stereo image super-resolution.