Video super-resolution is currently one of the most active research topics in computer vision as it plays an important role in many visual applications. Generally, video super-resolution contains a significant component, i.e., motion compensation, which is used to estimate the displacement between successive video frames for temporal alignment. Optical flow, which can supply dense and sub-pixel motion between consecutive frames, is among the most common ways for this task. To obtain a good understanding of the effect that optical flow acts in video super-resolution, in this work, we conduct a comprehensive review on this subject for the first time. This investigation covers the following major topics: the function of super-resolution (i.e., why we require super-resolution); the concept of video super-resolution (i.e., what is video super-resolution); the description of evaluation metrics (i.e., how (video) superresolution performs); the introduction of optical flow based video super-resolution; the investigation of using optical flow to capture temporal dependency for video super-resolution. Prominently, we give an in-depth study of the deep learning based video super-resolution method, where some representative algorithms are analyzed