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$Z_c(4430)$ discovered in $\bar{B}^0\to\psi(2S)K^-\pi^+$, $Z_c(4200)$ foundin $\bar{B}^0\to J/\psi K^-\pi^+$, and $Z_1(4050)$ and $Z_2(4250)$ observed in$\bar{B}^0\to\chi_{c1}K^-\pi^+$ are candidates of charged charmonium-likestates. All surviving theoretical models interpreted these candidates asfour-quark states, until we recently identified a compelling alternative. Wediscuss that kinematical singularities in triangle loop diagrams induce aresonance-like behavior that can consistently explain the properties (such asspin-parity, mass, width, and Argand plot) of $Z_c(4430)$, $Z_c(4200)$,$Z_1(4050)$ and $Z_2(4250)$ from experiments. In terms of the trianglesingularities, we can also naturally understand interesting experimentalfindings such as the appearance (absence) of $Z_c(4200)$($Z_c(4430)$)-likecontribution in $\Lambda_b^0\to J/\psi p\pi^-$, and the highly asymmetric shapeof the spectrum bump for $Z_1(4050)$; the other theoretical models have notsuccessfully addressed these points. Although Pakhlov et al. proposed anothertriangle diagram to generate a $Z_c(4430)$-like bump, we argue that thisscenario is very unlikely.

$Z_c(4430)$, $Z_c(4200)$, $Z_1(4050)$, and $Z_2(4250)$ as triangle singularities