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Super-resolution (SR) technique reconstructs a higher-resolution image or sequence from the observed LR images. As SR has been developed for more than three decades, both multi-frame and single-frame SR have significant applications in our daily life. This paper aims to provide a review of SR from the perspective of techniques and applications, and especially the main contributions in recent years. Regularized SR methods are most commonly employed in the last decade. Technical details are discussed in this article, including reconstruction models, parameter selection methods, optimization algorithms and acceleration strategies. Moreover, an exhaustive summary of the current applications using SR techniques has been presented. Lastly, the article discusses the current obstacles for future research.