Topology, a cornerstone of modern condensed matter physics, has in the past decade played a crucial role in diverse wave systems. As a powerful wave system, light can be sculpted into an even richer variety of topological structures, including vortices, skyrmions, Möbius strips, etc., leading to advanced photonic technologies from optical trapping to imaging, across quantum and classical regimes. A recent breakthrough demonstrated that topologically structured water waves can manipulate particles with intricate spin-orbital motion, and similar principles have enabled topological control in acoustofluidics, opening new insights in wave-matter interactions. Therefore, we argue that topological light waves possess an analogous potential, offering a route beyond the scalar-field limitations of conventional optical tweezers and establishing a new paradigm of multidimensional, vectorial control over matter. This article starts with brief introductions to optical tweezer technologies and topological light waves, then focuses on their emerging combination: particle trapping and sorting. It follows with perspectives on how topologies can couple to new degrees of freedom for manipulating complex particle motions previously inaccessible, and finally discusses potential applications.