  A glance at recent research on magnetism turns up a curious set of articles
discussing, or claiming evidence for, a state of matter called a quantum spin
liquid (QSL). These articles are notable in their invocation of exotic notions
of topological physics, quantum entanglement, fractional quantum numbers, anyon
statistics and gauge field theories. So what is a QSL and why do we need this
complicated technical vocabulary to describe it? Our aim in this article is to
introduce some of these concepts and provide a discussion of what a QSL is,
where it might occur in Nature and why it is of interest. As we'll see, this is
a rich subject which is still in development, and unambiguous evidence for the
realisation of the QSL state in a magnetic material remains hotly debated.
However, the payoff in terms of the special nature of quantum entanglement in
the QSL, and its diverse spectrum of unusual excitations and topological status
will (at least to some extent) justify the need to engage with some powerful,
occasionally abstract, technical material.
