Flow vector fields contain a wealth of information that needs to be visualized. As an extension of the well-known streamline technique, we have developed a context-based method for visualizing steady flow vector fields in two and three dimensions. We call our method "Priority Streamlines". In our approach, the density of the streamlines is controlled by a scalar function that can be user-defined, or be given by additional information (e.g., temperature, pressure, vorticity, velocity) considering the underlying flow vector field. In regions, which are interesting the streamlines are drawn with increased density, while less interesting regions are drawn sparsely. Since streamlines in the most important regions are drawn first, we can use thresholding to obtain a streamline representation highlighting essential features. Color-mapping and transparency can be used for visualizing other information hidden in the flow vector field.