This book chapter is published open access.
1+1-dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed, and manageable expressions thanks to the factorizability of the matrices which govern the scattering in these models. In particular, the correlation functions are expressed in terms of explicit series of multiple integrals, this nonperturbatively for all values of the coupling. However, the question of convergence of these series, and thus the mathematical well-definiteness of these correlators, is mostly open. This paper reviews the overall setting used to formulate such models and discusses the recent progress relative to solving the convergence issues in the case of the 1+1-dimensional massive integrable Sinh-Gordon quantum field theory.