Spectral Flow and Vortex Dynamics in Superfluids, Superconductors and Ferromagnets

We discuss the nondissipative Magnus-type force acting on linear defects in Fermi systems, such as Abrikosov vortices in superconductors, singular and continuous vortices in superfluid phases of $^3$He, magnetic vortices and skyrmions in ferromagnets. Spectral flow of fermion zero modes in the vortex core gives an essential contribution to the nondissipative force, which is confirmed in Manchester experiments on rotating $^3$He-B. The spectral flow effect is closely related to the angular momentum paradox.