Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum vacuum they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density atomic Bose-Einstein condensates as quantized vortex lines. We discuss unconventional vortices in unconventional superfluids and superconductors, which have been observed or have to be observed, such as continuous singly and doubly quantized vortices in 3 He-A and chiral Bose condensates; half-quantum vortices (Alice strings) in 3 He-A and in nonchiral Bose condensates; Abrikosov vortices with fractional magnetic flux in chiral and d-wave superconductors; vortex sheets in 3 He-A and chiral superconductors; the nexus – combined object formed by vortices and monopoles. PACS numbers: 1
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