  High-T_c superconductors in small magnetic fields directed away from the
crystal symmetry axes have been found to exhibit inhomogeneous chains of flux
lines (vortices), in contrast to the usual regular triangular flux-line
lattice. We review the experimental observations of these chains, and summarize
the theoretical background that explains their appearance. We treat separately
two classes of chains: those that appear in superconductors with moderate
anisotropy due to an attractive part of the interaction between tilted flux
lines, and those with high anisotropy where the tilted magnetic flux is created
by two independent and perpendicular crossing lattices. In the second case it
is the indirect attraction between a flux line along the layers (Josephson
vortex) and a flux line perpendicular to the layers (pancake vortex stack) that
leads to the formation of chains of the pancake vortex stacks. This complex
system contains a rich variety of phenomena, with several different equilibrium
phases, and an extraordinary dynamic interplay between the two sets of crossing
vortices. We compare the theoretical predictions of these phenomena with the
experimental observations made to date. We also contrast the different
techniques used to make these observations. While it is clear that this system
forms a wonderful playground for probing the formation of structures with
competing interactions, we conclude that there are important practical
implications of the vortex chains that appear in highly anisotropic
superconductors.
