  A review is presented of the Hall-Post inequalities that give lower-bounds to
the ground-state energy of quantum systems in terms of energies of smaller
systems. New applications are given for systems experiencing both a static
source and inner interactions, as well as for hydrogen-like molecules and for
tetraquarks in some quark models. In the latter case, the Hall-Post
inequalities constrain the possibility of deeply-bound exotic mesons below the
threshold for dissociation into two quark-antiquark mesons. We also emphasize
the usefulness of the Hall-Post bounds in terms of 3-body energies when some
2-body subsystems are ill defined or do not support any bound state.
