The development of high-performance electromagnetic interference (EMI) shielding materials is of great significance for preventing EM radiation. For traditional shielding materials, the pursuit of superior conductivity is the primary designing strategy to achieve highly efficient shielding performance. However, high conductivity will inevitably produce serious EM wave reflections and cause secondary EM radiation pollution. Therefore, absorption-dominated EMI shielding materials known as “green shielding materials” have become an ideal solution for conferring reliable EMI protection to next-generation electronics in complex EM environments. Conductive polymer composites (CPCs) as novel shielding materials have advantages in terms of flexible processability and adjustable EMI shielding performance, hence providing possibility to obtain absorption-dominated shielding materials. In this review, we introduce the evaluation method of absorption-dominated EMI shielding materials and discuss principles and strategies for designing efficient absorption-dominated shielding polymer composites. The recent advances of structural design approaches and processing methods of green shielding CPCs as well as the shielding mechanism of CPCs with low reflection shielding characteristics are systematically summarised. Major challenges of designing efficient EM wave dissipation structure are discussed and potential research frontiers in developing advanced absorption-dominated EMI shielding polymer composites are prospected. It is expected that green EMI shielding CPCs with high efficiency and long-term durability, favourable environmental adaptability as well as multifunctionality will eventually be widely used in the EM compatibility and protection of the next-generation electronic devices.