  We review some recent results concerning integrable quantum field theories in
1+1 space-time dimensions which contain unstable particles in their spectrum.
Recalling first the main features of analytic scattering theories associated to
integrable models, we subsequently propose a new bootstrap principle which
allows for the construction of particle spectra involving unstable as well as
stable particles. We describe the general Lie algebraic structure which
underlies theories with unstable particles and formulate a decoupling rule,
which predicts the renormalization group flow in dependence of the relative
ordering of the resonance parameters. We extend these ideas to theories with an
infinite spectrum of unstable particles. We provide new expressions for the
scattering amplitudes in the soliton-antisoliton sector of the elliptic
sine-Gordon model in terms of infinite products of q-deformed gamma functions.
When relaxing the usual restriction on the coupling constants, the model
contains additional bound states which admit an interpretation as breathers.
For that situation we compute the complete S-matrix of all sectors. We carry
out various reductions of the model, one of them leading to a new type of
theory, namely an elliptic version of the minimal SO(n)-affine Toda field
theory.
