The exciting discovery by LHCb of the $P_c(4312)^+$ and $P_c(4450)^+$ pentaquarks, or the suggestion of a tetraquark nature for the $Z_c(3900)$ state seen at BESIII and Belle, have triggered a lot of activity in the field of hadron physics, with new experiments planned for searching other exotic mesons and baryons, and many theoretical developments trying to disentangle the true multiquark nature from their possible molecular origin. After a brief review of the present status of these searches, this paper focusses on recently seen or yet to be discovered exotic heavy baryons that may emerge from a conveniently unitarized meson-baryon interaction model in coupled channels. In particular, we will show how interferences between the different coupled-channel amplitudes of the model may reveal the existence of a $N^*$ resonance around 2 GeV having a meson-baryon quasi-bound state nature. We also discuss the possible interpretation of some of the $Omega_c$ states recently discovered at LHCb as being hadron molecules. The model also predicts the existence of doubly-charmed quasibound meson-baryon $Xi_{cc}$ states, which would be excited states of the ground-state $Xi_{cc}(3621)$ MeV, whose mass has only been recently established. Extensions of these results to the bottom sector will also be presented.
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