Video super-resolution (VSR) is reconstructing high-resolution videos from low resolution ones. Recently, the VSR methods based on deep neural networks have made great progress. However, there is rarely systematical review on these methods. In this survey, we comprehensively investigate 37 state-of-the-art VSR methods based on deep learning. It is well known that the leverage of information contained in video frames is important for video super-resolution. Thus we propose a taxonomy and classify the methods into seven sub-categories according to the ways of utilizing inter-frame information. Moreover, descriptions on the architecture design and implementation details are also included. Finally, we summarize and compare the performance of the representative VSR methods on some benchmark datasets. We also discuss the applications, and 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 of the VSR techniques based on deep learning.