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apr11-offprint-stamp.pdf

We recall the modern view of quantum vortices as topological quantum solitons, in systems ranging from superfluids to hot neutron stars and the early universe. Outstanding problems associated with vortices are then reviewed, focussing on the form of vortex-quasiparticle interactions and the resulting vortex dynamics, and on the structure of vortices in the cuprate superconductors. A resolution of these questions, both theoretical and experimental, will have sweeping consequences for the phenomenology of both superfluids and superconductors, and indeed for our understanding of vortices in many other systems as well.