Helium has a decisive effect on the microstructure of silicon carbide materials after implantation and subsequent annealing. A dense population of bubbles and dislocation loops is already observed at relatively low displacement doses after annealing of helium-implanted \ensuremath{\alpha}-SiC, while no visible damage appears after irradiation without helium implantation under otherwise equal conditions. The defects are separated from grain boundaries by defect-free zones of approximately 0.5 \ensuremath{\mu}m width. The most intriguing features of the evolving microstructure are lenticular cavities (platelets), which transform to disk-shaped arrangements of bubbles with associated dislocation loops or even stacks of loops. The observed microstructural evolution and its dependence on implantation dose, annealing temperature, and time are quantitatively explained and discussed in terms of diffusion of interstitial He atoms and their clustering between adjacent lattice planes, thus forming nanocracks during implantation. The relaxation of the high gas pressure by matrix atom transfer from bubbles to loops during annealing and the coarsening of bubble-loop complexes are described by a coupled two-component Ostwald ripening process.