A number of candidate multiquark hadrons, i.e., particle resonances with substructures that are more complex than the quark-antiquark mesons and three-quark baryons that are prescribed in the textbooks, have recently been observed. In this talk I present: some recent preliminary BESIII results on the near-threshold behavior of sigma(e+e- --> Lambda Lambda-bar) that may or may not be related to multiquark mesons in the light- and strange-quark sectors; results from Belle and LHCb on the electrically charged, charmoniumlike Z(4430)^+ --> pi^+ psi resonance that necessarily has a four-quark substructure; and the recent LHCb discovery of the P_c(4380) and P_c(4450) hidden-charm resonances seen as a complex structure in the J/psi p invariant mass distribution for Lambda_b --> K^-J/psi p decays and necessarily have a five-quark substructure and are, therefore, prominent candidates for pentaquark baryons.
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