Flow maps are an established cartographic method to depict movements over time and space. In recent years, the exponential increase of geospatial information – what we could call urban ‘big data’ – has introduced new use cases and highlighted the need to expand cartography. In this paper, we define existing visualization strategies and tools, and examine their characteristics. From this, we identify challenges and opportunities for data-driven flow maps and suggest future developments. Specifically, we apply a new taxonomy to compare several geospatial data visualizations from the MIT Senseable City Lab and extract principles that can define the capabilities of a new interactive flow mapping tool. We have begun to work on such a tool – called the Datacollider – that is public, powerful, intuitive, and scalable. In the latter portion of this paper, we describe the Datacollider, articulate its limitations, and outline directions for future development. We conclude by extrapolating broader trends for the field of geospatial data visualization. We articulate a shift from visualization as a set of graphic tools for representing found insights, to visualization as a way of engaging with data and deriving knowledge.