  The advent of graphene and other two-dimensional van der Waals materials,
with their unique electrical, optical, and thermal properties, has resulted in
tremendous progress for fundamental science. Recent developments suggest that
taking one more step down in dimensionality - from monolayer, atomic sheets to
individual atomic chains - can bring exciting prospects as the ultimate limit
in material downscaling is reached while establishing an entirely new field of
one-dimensional quantum materials. Here we review this emerging area of
one-dimensional van der Waals quantum materials and anticipate its future
directions. We focus on quantum effects associated with the charge-density-wave
condensate, strongly-correlated phenomena, topological phases, and other unique
physical characteristics, which are attainable specifically in van der Waals
materials of lower dimensionality. Possibilities for engineering the properties
of quasi-one-dimensional materials via compositional changes, vacancies, and
defects, as well as the prospects of their applications in composites are also
discussed.
