  The quark model was formulated in 1964 to classify mesons as bound states
made of a quark-antiquark pair, and baryons as bound states made of three
quarks. For a long time all known mesons and baryons could be classified within
this scheme. Quantum Chromodynamics (QCD), however, in principle also allows
the existence of more complex structures, generically called exotic hadrons or
simply exotics. These include four-quark hadrons (tetraquarks and hadronic
molecules), five-quark hadrons (pentaquarks) and states with active gluonic
degrees of freedom (hybrids), and even states of pure glue (glueballs). Exotic
hadrons have been systematically searched for in numerous experiments for many
years. Remarkably, in the past fifteen years, many new hadrons that do not
exhibit the expected properties of ordinary (not exotic) hadrons have been
discovered in the quarkonium spectrum. These hadrons are collectively known as
$XYZ$ states. Some of them, like the charged states, are undoubtedly exotic.
Parallel to the experimental progress, the last decades have also witnessed an
enormous theoretical effort to reach a theoretical understanding of the $XYZ$
states. Theoretical approaches include not only phenomenological extensions of
the quark model to exotics, but also modern non-relativistic effective field
theories and lattice QCD calculations. The present work aims at reviewing the
rapid progress in the field of exotic $XYZ$ hadrons over the past few years
both in experiments and theory. It concludes with a summary on future prospects
and challenges.
