Recent developments in reservoir characterization and in the management of uncertainty have lead to the ability of the petroleum industry to routinely generate large, multimillion-cell detailed geologic models. This has resulted in a steadily increasing gap between flow simulation and the static model, not only because of the size of these models, but also because of our desire to obtain reservoir performance predictions for multiple realizations of such models. Three-dimensional streamline-based computation offers significant potential to meet some of these challenges, leading to a rapidly developing technology. The purpose of this paper is to review current streamline technology: its foundations (the ＇time of flight＇ formulation), historical precedents (streamtubes and front trackers), current applications, open questions, and potential limitations. A wide range of applications will be used to demonstrate the utility of both streamline simulation and the underlying formulation. Where required, new material will be presented (analysis of field tracer response, streamline modeling in corner point cells, evaluation of grid orientation effects, discussion of open questions). Otherwise, existing results will be drawn from the literature.