  Vortex states of photons, electrons, and other particles are non--plane-wave
solutions of the corresponding wave equation with helicoidal wave fronts. These
states possess an intrinsic orbital angular momentum with respect to the
average propagation direction, which represents a new degree of freedom,
previously unexplored in particle or nuclear collisions. Vortex states of
photons, electrons, neutrons, and neutral atoms have been experimentally
produced, albeit at low energies, and are being intensively explored.
Anticipating future experimental progress, one can ask what additional insights
on nuclei and particles one can gain once collisions of high-energy vortex
states become possible. This review describes the present-day landscape of
physics opportunities, experimental progress and suggestions relevant to vortex
states in high energy collisions. The aim is to familiarize the community with
this emergent cross-disciplinary topic and to provide a sufficiently complete
literature coverage, highlighting some results and calculational techniques.
