Three-particle scattering amplitudes from lattice QCD

Three-particle observables are the present frontier in lattice QCD scattering calculations. In this talk, I will report on the extraction of three-particle scattering amplitudes from lattice simulations. I will review the existing theoretical approaches and their relation, and comment on recent generalizations to include nonidentical particles and three-particle resonances. I will also address the current status of lattice simulations, including novel results in the $\varphi^4$ theory, and for three charged pions in QCD.