The studies on the space of flow play an important role in understanding the structure and change of urban networks. The rapid development of big data provides new opportunities and challenges for the studies on the space of flow in recent years. This article systematically reviewed the research progress on the space of flow based on big data. First, we retrospect the background and history of the studies on the space of flow, then summarized the themes, the types of big data, the methods used for the studies and the major findings, as well as discussed the research challenges. We found an exponential growth of studies on the space of flow using big data after 2011. The annual number of published papers increased from 11 to 106 during 2011-2018. Big data deepen the research on the space of flow by providing new data sources, inspiring new analytical methods, and new research perspectives. Four types of big data—mobile phone, social media, smart card, and taxi trajectory data are commonly used in the studies on the space of flow, which can provide information on spatiotemporal flows (such as population flow, material flow, and information flow) directly. Research methods have also evolved from distance-based gravity models to network analysis. In the future, the research on the space of flow using big data can be further improved by validating the effectiveness and representativeness of the big data, the integration of big data and traditional data, and the information mining from big data using new methods such as deep learning and cloud computing.