  We study the spectrum of massive excitations in three-dimensional models
belonging to the Ising universality class. By solving the Bethe-Salpeter
equation for 3D $\phi^4$ theory in the broken symmetry phase we show that
recently found non-perturbative states can be interpreted as bound states of
the fundamental excitation. We show that duality predicts an exact
correspondence between the spectra of the Ising model in the broken symmetry
phase and of the Z(2) gauge theory in the confining phase. The interpretation
of the glueball states of the gauge theory as bound states of the dual spin
system allows us to explain the qualitative features of the glueball spectrum,
in particular, its peculiar angular momentum dependence.
