In this paper, we review the main results concerning the first instabilities, characterised by the breaking of spatio-temporal symmetries, occurring in the wake of bluff bodies, as the flow speed is increased. Phenomenological wake models are compared to experiments for the geometry of a circular cylinder and of a sphere. The transition from a cylindrical to spherical configuration is also illustrated in various ways, such as the transverse coupling of two sphere wakes and a reduction in length or a wavy deformation of a circular cylinder. Finally, we report preliminary results concerning the fluid-structure interactions in the case of a longitudinally tethered sphere.