The advanced electrochemical properties, such as high energy density, fast charge–discharge rates, excellent cyclic stability, and specific capacitance, make supercapacitor a fascinating electronic device. During recent decades, a significant amount of research has been dedicated to enhancing the electrochemical performance of the supercapacitors through the development of novel electrode materials. In addition to highlighting the charge storage mechanism of the three main categories of supercapacitors, including the electric double-layer capacitors (EDLCs), pseudocapacitors, and the hybrid supercapacitors, this review describes the insights of the recent electrode materials (including, carbon-based materials, metal oxide/hydroxide-based materials, and conducting polymer-based materials, 2D materials). The nanocomposites offer larger SSA, shorter ion/electron diffusion paths, thus improving the specific capacitance of supercapacitors (SCs). Besides, the incorporation of the redox-active small molecules and bio-derived functional groups displayed a significant effect on the electrochemical properties of electrode materials. These advanced properties provide a vast range of potential for the electrode materials to be utilized in different applications such as in wearable/portable/electronic devices such as all-solid-state supercapacitors, transparent/flexible supercapacitors, and asymmetric hybrid supercapacitors.