2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225538We shortly recall the derivation of the Faddeev-Yakubovsky differential equations and point out their main advantages. Then we give a review of the numerical approaches used to solve the bound-state and scattering problems for the three- and four-body systems based on these equations. A particular attention is payed to the latest developments.A review article based on a talk given at the 20th European Conference on Few-Body Problems in PhysicsQuantum PhysicsMathematical PhysicsNuclear Theorytext