Abstract: Data compression has been an important research issue in the area of visualization. With the rapidly increasing of dimensions、resolutions and variables, the amount of volume data is growing exponentially, which makes compression become even more significant today. In this paper, We summarize the related works on the volume compression including lossless and lossy ones. Firstly, We compare the advantages and disadvantages in various lossless algorithms. Then a general flow and several key stages in lossy compression are presented, followed by a detailed introduction of time-varying data compression. In the end, We discuss the future research on this topic.