  For many decades after the invention of the quark model in 1964 there was no
evidence that hadrons are formed from anything other than the simplest pairings
of quarks and antiquarks, mesons being formed of a quark-antiquark pair and
baryons from three quarks. In the last decade, however, in an explosion of data
from both $e^+e^-$ and hadron colliders, there are many recently observed
states that do not fit into this picture. These new particles are called
generically "exotics". They can be either mesons or baryons. Remarkably, they
all decay into at least one meson formed of either a $c\overline{c}$ or
$b\overline{b}$ pair. In this review, after the introduction, we explore each
of these new discoveries in detail first from an experimental point of view,
then subsequently give a theoretical discussion. These exotics can be explained
if the new mesons contain two-quarks and two-antiquarks (tetraquarks), while
the baryons contain four-quarks plus an antiquark (pentquarks). The theoretical
explanations for these states take three divergent tracks: tightly bound
objects, just as in the case of normal hadrons, but with more constituents, or
loosely bound "molecules" similar to the deuteron, but formed from two mesons,
or a meson or baryon, or more wistfully, they are not multiquark states but
appear due to kinematic effects caused by different rescatterings of virtual
particles; most of these models have all been post-dictions. Both the tightly
and loosely bound models predict the masses and related quantum numbers of new,
as yet undiscovered states. Thus, future experimental discoveries are needed
along with theoretical advances to elucidate the structure of these new exotic
states.
