This paper deals with numerical simulations on a self-propelled fish-like body. Firstly, the methods used to achieve such simulations based on the solution of the Reynolds-Averaged-Navier–Stokes Equations are described: resolution of the Newton's law (parameterization, use of a description of the rotation based on a quaternion), regridding strategies linked to body motion and deformation, fluid–motion coupling methods. In the second part, realistic applications are shown. The interaction between the fluid and the body is fully solved since the evolution of the body's position is not imposed but computed. Only the imposed deformation of the shape and its interaction with the fluid produce forces on the body and, consequently, motion.