The past 15 years have seen the expansion in the classes of experimentally observed hadrons to include not only mesons and baryons, but tetraquarks and pentaquarks as well.  We begin with a brief summary of their discovery, where they fit into the scheme of known hadrons, and their current experimental status.  The exact nature of their structure remains completely unresolved, and we propose a paradigm in which the exotics are composed of diquarks that are bound not like molecules, but solely by confinement.  The question then becomes how to describe such states, and we argue that the Born-Oppenheimer (B-O) approximation provides the best way forward.  Starting with B-O quantum numbers that are relevant for exotics, we develop the multiplets of the expected lowest-lying states, as well as their decay selection rules, in order to compare with experiment.   We conclude by identifying the wide variety of detailed, predictive calculations that will be carried out using this formalism in the future.