An overview of the Magnus effect of projectiles and missiles is presented. The first part of the paper is devoted to the description of the physical mechanisms governing the Magnus effect. For yawing and spinning projectiles, at small incidences, the spin induces a weak asymmetry of the boundary layer profiles. At high incidences, increased spin causes the separated vortex sheets to be altered. Vortex asymmetry generates an additional lateral force which gives a vortex contribution to the total Magnus effect. For finned projectiles or missiles, the origin of the Magnus effect on fins is the main issue. There are two principal sources contributing to the Magnus effect. Firstly, the interaction between the asymmetric boundary layer-wake of the body and the fins, and secondly, the spin induced modifications of the local incidences and of the flow topology around the fins. The second part of the paper is devoted to the numerical prediction and validation of these flow phenomena. A state of the art is presented including classical CFD methods based on Reynolds-averaged Navier–Stokes (RANS) and unsteady rans (URANS) equations, and also hybrid RANS/LES approach called ZDES. This last method is a recent advance in turbulence modeling methodologies that allows to take into account the unsteadiness of the flow in the base region. For validation purposes computational results were compared with wind tunnel tests. A wide range of angles of attack, spin rates, Reynolds and Mach numbers (subsonic, transonic and supersonic) have been investigated.