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In recent years, deep learning has made great progress in many fields such as image recognition, natural language processing, speech recognition and video super-resolution. In this survey, we comprehensively investigate 33 state-of-the-art video super-resolution (VSR) methods based on deep learning. It is well known that the leverage of information within video frames is important for video super-resolution. Thus we propose a taxonomy and classify the methods into six sub-categories according to the ways of utilizing inter-frame information. Moreover, the architectures and implementation details of all the methods are depicted in detail. Finally, we summarize and compare the performance of the representative VSR method on some benchmark datasets. We also discuss some challenges, which need to be further addressed by researchers in the community of VSR. To the best of our knowledge, this work is the first systematic review on VSR tasks, and it is expected to make a contribution to the development of recent studies in this area and potentially deepen our understanding to the VSR techniques based on deep learning.