Polymer matrix composites have generated a great deal of attention in recent decades in various fields due to numerous advantages polymer offer. The advancement of technology has led to stringent requirements in shielding materials as more and more electronic devices are known to cause electromagnetic interference (EMI) in other devices. The drive to fabricate alternative materials is generated by the shortcomings of the existing metallic panels. While polymers are more economical, easy to fabricate, and corrosion resistant, they are known to be inherent electrical insulators. Since high electrical conductivity is a sought after property of EMI shielding materials, polymers with fillers to increase their electrical conductivity are commonly investigated for EMI shielding. Recently, composites with nanofillers also have attracted attention due to the superior properties they provide compared to their micro counterparts. In this review polymer composites with various types of fillers have been analysed to assess the EMI shielding properties generated by each. Apart from the properties, the manufacturing processes and morphological properties of composites have been analysed in this review to find the best polymer matrix composites for EMI shielding.