Real-time hadron scattering amplitudes can be computed from Euclidean lattice QCD simulations by studying multi-hadron energy levels in a finite volume. Advances in algorithms for treating quark propagation have paved the way for recent improvements in computing these energies, resulting in rapid progress in lattice calculations of scattering amplitudes. Many two-meson amplitudes have already been determined precisely, while considerable progress is being made for meson-baryon and baryon-baryon systems. I will review recent results for elastic scattering amplitudes between pseudo-scalar mesons before discussing prospects for the simplest meson-baryon and baryon-baryon systems.

Finally, I will discuss recent formal developments in computing scattering amplitudes from lattice QCD spectral functions; an approach in which the infinite-volume volume limit is taken at the outset.