The constantly improving resolution of geophysical data, seismic tomography and seismicity in particular, shows that the lithosphere does not subduct as a slab of uniform thickness but is rather thinned in the upper mantle and thickened around the transition zone between the upper and lower mantle. This observation has traditionally been interpreted as evidence for the buckling and piling of slabs at the boundary between the upper and lower mantle, where a strong contrast in viscosity may exist and cause resistance to the penetration of slabs into the lower mantle. The distribution and character of seismicity reveal, however, that slabs undergo vertical extension in the upper mantle and compression near the transition zone. In this paper, we demonstrate that during the subduction process, the shape of low viscosity slabs (1 to 100 times more viscous than the surrounding mantle) evolves toward an inverted plume shape that we coin jellyfish. Results of a 3D numerical model show that the leading tip of slabs deform toward a rounded head skirted by lateral tentacles that emerge from the sides of the jellyfish head. The head is linked to the body of the subducting slab by a thin tail. A complete parametric study reveals that subducting slabs may achieve a variety of shapes, in good agreement with the diversity of natural slab shapes evidenced by seismic tomography. Our work also suggests that the slab to mantle viscosity ratio in the Earth is most likely to be lower than 100. However, the sensitivity of slab shapes to upper and lower mantle viscosities and densities, which remain poorly constrained by independent evidence, precludes any systematic deciphering of the observations.