Recent progress on multifunctional electromagnetic interference shielding polymer composites

•The review discusses the basic theory, attenuation mechanisms and characterization methods of electromagnetic interference (EMI) shielding.•The recent progress of multifunctional EMI shielding polymer composites are summarized and discussed with respect to their structures, fabrication methods and specific functions.•The critical scientific and technical issues for EMI shielding composites with different functions are proposed, and the main challenges in the development of multifunctional polymer-based EMI shielding materials are presented.