The early 1960s witnessed a wealth of elementary particles described in terms of simple combinations of a few more elementary units, dubbed quarks. The known mesons and baryons could all be described as states of quark-antiquark or three quarks. However, it was not understood why certain more elaborate combinations, such as (two quarks + two antiquarks) or (four quarks + one antiquark) had not been observed. It has taken nearly half a century, but these “exotic” particles are now beginning to be seen and understood. This colloquium will trace their discovery and interpretation, with an eye to their future study.