Three-body dynamics plays a relevant role for the decay of excited mesons and baryons, including exotics and hybrids searched for at GlueX, COMPASS and other experiments. The calculation of these systems from lattice QCD is equally relevant. Three-body effects influence Dalitz plots and finite-volume energy levels, respectively, and they have to be taken into account. Using the S-matrix principle of unitarity, a formalism is presented that can be used to analyze experimental data and lattice data. It is illustrated in applications to the a1(1260) meson and for mesonic systems at maximal isospin from lattice QCD. A substantial part of the presentation is dedicated to an introduction of the physics principles that can be followed by graduate students familiar with the basics of quantum mechanical scattering theory.
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