Numerical Lattice QCD calculations are necessarily performed in a finite volume and with Euclidean time. For scattering and transition amplitudes these constraints have important consequences. In particular, it is not possible to directly access such amplitudes from numerically determined Euclidean correlators. In the past decades, great progress has been made to overcome this limitation 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.