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Dataframes are a popular abstraction to represent, prepare, and analyze data. Despite the remarkable success of dataframe libraries in Rand Python, dataframes face performance issues even on moderately large datasets. Moreover, there is significant ambiguity regarding dataframe semantics. In this paper we lay out a vision and roadmap for scalable dataframe systems. To demonstrate the potential in this area, we report on our experience building MODIN, a scaled-up implementation of the most widely-used and complex dataframe API today, Python's pandas. With pandas as a reference, we propose a simple data model and algebra for dataframes to ground discussion in the field. Given this foundation, we lay out an agenda of open research opportunities where the distinct features of dataframes will require extending the state of the art in many dimensions of data management. We discuss the implications of signature data-frame features including flexible schemas, ordering, row/column equivalence, and data/metadata fluidity, as well as the piecemeal, trial-and-error-based approach to interacting with dataframes.