  Few-body hadronic observables play an essential role in a wide number of
processes relevant for both particle and nuclear physics. In order for Lattice
QCD to offer insight into the interpretation of few-body states, a theoretical
infrastructure must be developed to map Euclidean-time correlation functions to
the desired Minkowski-time few-body observables. In this talk, I review the
formal challenges associated with the studies of such systems via Lattice QCD,
as first introduced by Maiani and Testa, and I also review the methodology to
circumvent said limitations. The first main example of the latter is the
formalism by Luscher to analyze elastic scattering and a second is the method
by Lellouch and Luscher to analyze weak decays. I discus recent theoretical
generalizations of these frameworks that allow for the determination of
scattering amplitudes, resonances, nonlocal contribution to matrix elements,
and form factors below and above inelastic thresholds. Finally, I outline
outstanding problems, including those that are now beginning to be addressed.
