  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.
