Three-body amplitudes for the analysis of lattice data and experiment

Hadronic resonances are emergent phenomena of Quantum Chromodynamics at intermediate energies. Almost all resonances decay not only to two, but also to three or more particles.
Parametrizing three-body dynamics in terms of unitary coupled-channel amplitudes is, therefore, a prerequisite for the extraction of resonances from experiment and also from finite-volume lattice QCD spectra. In the talk, construction principles, examples, and applications for three-body amplitudes will be presented, including the axial a1(1260) and its three-pion dynamics, its determination from lattice QCD, and recent extensions to strangeness channels and complex energies, as well as connections to triangle singularities.