The most common type of insulation of extruded high‐voltage power cables is composed of low‐density polyethylene (LDPE), which must be crosslinked to adjust its thermomechanical properties. A major drawback is the need for hazardous curing agents and the release of harmful curing byproducts during cable production, while the thermoset nature complicates reprocessing of the insulation material. This perspective explores recent progress in the development of alternative concepts that allow to avoid byproducts through either click chemistry type curing of polyethylene‐based copolymers or the use of polyolefin blends or copolymers, which entirely removes the need for crosslinking. Moreover, polypropylene‐based thermoplastic formulations enable the design of insulation materials that can withstand higher cable operating temperatures and facilitate reprocessing by remelting once the cable reaches the end of its lifetime. Finally, polyethylene‐based covalent and non‐covalent adaptable networks are explored, which may allow to combine the advantages of thermoset and thermoplastic insulation materials in terms of thermomechanical properties and reprocessability.