Explore optimization challenges in magnetic confinement for stellarator fusion reactors in this 39-minute conference talk from the Workshop on "New perspective on Shape and Topology Optimization" at the Erwin Schrödinger International Institute. Delve into the physical context and industrial motivations behind stellarator design, examine modeling issues related to magnetic forces, and discover theoretical and numerical findings on shape optimization for optimal coil design. If time allows, investigate the existence of optimal shapes under uniform reach constraints, gaining valuable insights into cutting-edge nuclear fusion research and development.