As JLab completes its 12 GeV upgrade, the coming years are expected to bring major developments in our understanding of the strong force. To get the most out of upcoming experiments, it is crucial to have solid theory predictions, based in the underlying theory of QCD. Here the well established methods of Lattice QCD should play a key role. However, numerical Lattice QCD calculations are necessarily performed in a finite volume and with Euclidean time and for scattering and transition amplitudes these constraints have important consequences. It is not possible to directly access the desired observables from the numerically determined correlators. Nonetheless, great progress has been made by using finite volume as a tool rather than an artifact, and deriving non-perturbative relations between the finite- and infinite-volume theories. I will review recent developments in this work with particular focus on three-hadron final states.