  Recent discoveries by Belle and BESIII of charged exotic quarkonium-like
resonances provide fresh impetus for study of heavy exotic hadrons. In the
limit N_c --> infinity, M_Q --> infinity, the (Qbar Q qbar q') tetraquarks
(TQ-s) are expected to be narrow and slightly below or above the (Qbar q') and
(Q qbar) two-meson threshold. The isoscalar TQ-s manifest themselves by decay
to (Qbar Q) pi pi, and the ~30 MeV heavier charged isotriplet TQ-s by decays
into (Qbar Q) pi. The new data strongly suggest that the real world with N_c=3,
Q=c,b and q,q' = u,d is qualitatively described by the above limit. We discuss
the relevant theoretical estimates and suggest new signatures for TQ-s in light
of the recent discoveries. We also consider "baryon-like" states (Q Q' qbar
qbar'), which if found will be direct evidence not just for near-threshold
binding of two heavy mesons, but for genuine tetraquarks with novel color
networks. We stress the importance of experimental search for doubly-heavy
baryons in this context.
