Advancements in technology and widespread usage of electronic equipment have led to a vast hike in electromagnetic pollution such as electromagnetic interference (EMI). This has resulted in major concerns regarding human health and improper functioning of electronic devices. Therefore, high-performance EMI shielding materials are necessary to ensure human well-being and protect systems in domestic, civil, or military applications. Earlier, metals and alloys of metals served as EMI shielding materials. But due to their heavy weight, low corrosion resistance, and advancements in miniaturization of electronic devices, currently, metals have only restricted applications in EMI shielding. Thus, flexible, lightweight, and high-performance EMI shielding materials assume great significance. Polymer composites have emerged as a better alternative to EMI shielding materials because of their light weight, corrosion resistance, and ease of fabrication. This article reviews the important literature on electrospun polymer composite fibers for EMI shielding applications. Fabrication methods and different types of fillers and their influence on EMI shielding properties are discussed in detail. The article tries to highlight the huge potential of the electrospinning technique toward the development of specialty materials for EMI shielding.