Linens defects are generic in continuous media. In quantum systems they app
ear as topological line defects which are associated! with a circulating pe
rsistent current. In relativistic quantum vacuum they an known as cosmic st
rings, in superconductors as quantized flux fines, and in superfluids and l
ow-density atomic Bose-Einstein condensates as quantized vortex lines. We d
iscuss unconventional vortices in unconventional superfluids and supercondu
ctors, which have been observed or have to be observed, such as continuous
singly and doubly quantized vortices in He-3-A and chiral Bose condensates;
half-quantum vortices (Alice strings) in He-3-A and in nonchiral Bose cond
ensates; Abrikosov vortices with fractional magnetic flux in chiral and d-w
ave superconductors; vortex sheets in He-3-A and chiral superconductors; th
e nexus combined object formed by vortices and monopoles. Some properties o
f vortices related to the fermionic quasiparticles living in the vortex cor
e are also discussed.