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Effective 3D streamline placement and visualization play an essential role in many science and engineering disciplines. The main challenge for effective streamline visualization lies in seed placement, i.e., where to drop seeds and how many seeds should be placed. Seeding too many or too few streamlines may not reveal flow features and patterns either because it easily leads to visual clutter in rendering or it conveys little information about the flow field. Not only does the number of streamlines placed matter, their spatial relationships also play a key role in understanding the flow field. Therefore, effective flow visualization requires the streamlines to be placed in the right place and in the right amount. This paper introduces hierarchical streamline bundles, a novel approach to simplifying and visualizing 3D flow fields defined on regular grids. By placing seeds and generating streamlines according to flow saliency, we produce a set of streamlines that captures important flow features near critical points without enforcing the dense seeding condition. We group spatially neighboring and geometrically similar streamlines to construct a hierarchy from which we extract streamline bundles at different levels of detail. Streamline bundles highlight multiscale flow features and patterns through clustered yet not cluttered display. This selective visualization strategy effectively reduces visual clutter while accentuating visual foci, and therefore is able to convey the desired insight into the flow data.