  In the context of constructing interacting quantum field theories in the
operator-algebraic approach, wedge-local fields play an important role. After
the work of Lechner to construct factorizing scattering matrix models with
scalar S-matrices without bound states, we recently extended this construction
to a class of models with a richer particle spectrum and which are believed to
have bound states. These include the Z(N)-Ising model and the affine-Toda field
theories. This construction is done by exhibiting wedge-local fields which
arise as a deformation of Lechner's fields with the so called "bound state
operator". I will review the main passages of this construction and explain the
open problems.
