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I describe recent progress in calculating scattering amplitudes and resonance properties involving two and three particles using lattice QCD. Formalism has been derived, using QFT in finite and infinite volumes, that relates the finite-volume spectrum to scattering amplitudes.
I describe the status of this formalism, and present selected applications using spectra determined using lattice QCD. I close with a discussion of unresolved issues and provide an outlook for future extensions of this work.