Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. By constructing a nonrelativistic effective field theory with open channels, we discuss the generalities of threshold behavior, and offer an explanation of the abundance of near-threshold peaks in the heavy quarkonium regime. We show that the threshold cusp can show up as a peak only for channels with attractive interaction, and the width of the cusp is inversely proportional to the reduced mass relevant for the threshold. We argue that there should be threshold structures at any threshold of a pair of heavy-quark and heavy-antiquark hadrons, which have attractive interaction at threshold, in the invariant mass distribution of a heavy quarkonium and light hadrons that couple to that open-flavor hadron pair. The structure becomes more pronounced if there is a near-threshold pole. Then, to get an overall feature of the spectrum of hadronic molecules composed of a pair of heavy-antiheavy hadrons, namely, which pairs are possible to form molecular states,we approximate the near-threshold interaction by the resonance saturation with the light-vector exchanges. In total, 229 molecular states are predicted. The observed near-threshold structures with hidden-charm, like the famous X(3872)X(3872) and P_cP_c states, fit into the spectrum we obtain. Lots of the predicted states are to be explored experimentally.
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