I introduce an entirely new dynamical description for exotic charmoniumlike hadrons, based upon the competing effects of the strong attraction between quarks in a diquark, and the inability of the diquark to hadronize on its own due to being a color nonsinglet. This mechanism naturally explains, for example, the strong preference of the Z(4475) to decay to psi(2S) rather than the J/psi, the existence of a state X(4630) that decays to Lambda_c baryon pairs, and why some but not all exotics lie near hadronic thresholds. Owing to high-energy constituent counting rules, the four-quark nature of the states produces major changes to both the high-s scaling of cross sections for producing such states and to the potency of the cusp effect of attracting resonances to pair-production thresholds. The recently observed P_c^+ pentaquark candidates are seen to fit naturally into this scheme.