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This review represents a comprehensive study of nanocomposites for power cables insulations based on thermoplastic polymers such as polyethylene congeners like LDPE, HDPE and XLPE, which is complemented by original results. Particular focus lies on the structure-property relationships of nanocomposites and the materials' design with the corresponding electrical properties. The critical factors, which contribute to the degradation or improvement of the electrical performance of such cable insulations, are discussed in detail; in particular, properties such as electrical conductivity, relative permittivity, dielectric losses, partial discharges, space charge, electrical and water tree resistance behavior and electric breakdown of such nanocomposites based on thermoplastic polymers are described and referred to the composites' structures. This review is motivated by the fact that the development of polymer nanocomposites for power cables insulation is based on understanding more closely the aging mechanisms and the behavior of nanocomposites under operating stresses.