The motion of vortices has been an area of study for more than a century. During the classical period of vortex dynamics, from the late 1800s, many interesting properties of vortices were discovered, beginning with the notable Kelvin waves propagating along an isolated vortex line (Thompson, 1880). The main object of theoretical studies at that time was a dissipationless perfect fluid (Lamb, 1997). It was difficult for the theory to find a common ground with experiment since any classical fluid exhibits viscous effects. The situation changed after the works of Onsager (1949) and Feynman (1955) who revealed that rotating superfluids are threaded by an array of vortex lines with quantised circulation. With this discovery, the quantum period of vortex dynamics began. Rotating superfluid 4He provided the testing ground for the theories of vortex motion developed for the perfect fluid. At the same time, some effects needed an extension of the theory to include twofluid effects, and the quantum period of vortex studies was marked by progress in the understanding of vortex dynamics in the framework of the two-fluid theory. The first step in this direction was taken by Hall and Vinen (1956a), who introduced the concept of mutual friction between vortices and the normal part of the superfluid and derived the law of vortex motion in two-fluid hydrodynamics. Hall (1958) and Andronikashvili et al. (1961) were the first to study experimentally the elastic properties of vortex lines using torsional oscillators. This made it possible to observe Kelvin waves with a spectrum modified by the interaction between vortices. Elastic deformations of vortex lines were caused by pinning of vortices at solid surfaces confining the superfluid. Vortex pinning was another important concept, which emerged during the study of dynamics of quantised vortices.

The third important theoretical framework, invented to describe vortex motion in rotating superfluids, was so-called macroscopic hydrodynamics. This relied on a coarse-graining procedure of averaging hydrodynamical equations over scales much larger than the intervortex spacing. Such hydrodynamics was used in the pioneering work on dynamics of superfluid vortices by Hall and Vinen (1956a) and further developed by Hall (1960) and Bekarevich and Khalatnikov (1961). It was a continuum theory similar to the elasticity theory. However, it only included bending deformations of vortex lines and ignored the crystalline order of the vortex array.