A few years ago, we initiated a research program to investigate the finite volume behaviour of matrix elements of local operators (form factors) in quantum field theory. The testing ground of these ideas is provided by integrable field theories such as the Lee-Yang, Ising and sine-Gordon models. The framework we developed can be used to provide a non-perturbative numerical method to determine form factors, or to verify bootstrap form factor solutions against the field theory dynamics. It also serves as a theoretical tool to construct spectral expansions of correlation functions in a thermal bath or in a boundary setting, relevant to condensed matter problems. In addition, it gives us a way to address questions of potential interest to lattice QCD. I plan to review the framework and its applications in a pedagogical manner, and to discuss briefly the latest developments.
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