The extraction of scattering amplitudes from lattice QCD simulations is reaching a mature stage. In this talk, I will review the well-established two-particle finite-volume scattering formalism. I will show how this can be used in practice, and I will comment some of our recent results for isospin-2 pion scattering at the physical point. I will also discuss the status of the formalism for the computation of three-particle scattering amplitudes from the lattice, which is becoming a hot topic in the lattice QCD community.