Because of gravitational interactions with their companions, the rotational dynamics of planets and stars involve periodic perturbations of their shape, the direction of their rotational vector, and their rotation rate. These perturbations correspond in planetary terms to tides, precession, and longitudinal libration. We review here the flows driven by those mechanical forcings on rotating spheres and ellipsoids. Special focus is placed on the associated instabilities and on the various routes toward turbulence recently studied. The key point is that mechanical forcings do not provide the energy to the excited flows: They convey part of the available rotational energy and generate intense fluid motions through the excitation of localized jets, shear layers, and resonant inertial modes. Hence, even very small forcings may have large-scale consequences. Mechanically driven flows thus play a fundamental role in planets and stars, significantly influencing their shape, their rotational dynamics, and their magnetic field.