Video segmentation, i.e., partitioning video frames into multiple segments or objects, plays a critical role in a broad range of practical applications, e.g., visual effect assistance in movie, scene understanding in autonomous driving, and virtual background creation in video conferencing, to name a few. Recently, due to the renaissance of connectionism in computer vision, there has been an influx of numerous deep learning based approaches that have been dedicated to video segmentation and delivered compelling performance. In this survey, we comprehensively review two basic lines of research in this area, i.e., generic object segmentation (of unknown categories) in videos and video semantic segmentation, by introducing their respective task settings, background concepts, perceived need, development history, and main challenges. We also provide a detailed overview of representative literature on both methods and datasets. Additionally, we present quantitative performance comparisons of the reviewed methods on benchmark datasets. At last, we point out a set of unsolved open issues in this field, and suggest possible opportunities for further research.