Supercapacitors have gained significant attention owing to their exceptional performance in terms of energy density and power density, making them suitable for various applications, such as mobile devices, electric vehicles, and renewable energy storage systems. This review focuses on recent advancements in the utilization of 0-dimensional to 3-dimensional carbon network materials as electrode materials for high-performance supercapacitor devices. This study aims to provide a comprehensive evaluation of the potential of carbon-based materials in enhancing the electrochemical performance of supercapacitors. The combination of these materials with other cutting-edge materials, such as Transition Metal Dichalcogenides (TMDs), MXenes, Layered Double Hydroxides (LDHs), graphitic carbon nitride (g-C3N4), Metal–Organic Frameworks (MOFs), Black Phosphorus (BP), and perovskite nanoarchitectures, has been extensively studied to achieve a wide operating potential window. The combination of these materials synchronizes their different charge-storage mechanisms to attain practical and realistic applications. The findings of this review indicate that hybrid composite electrodes with 3D structures exhibit the best potential in terms of overall electrochemical performance. However, this field faces several challenges and promising research directions. This study aimed to highlight these challenges and provide insights into the potential of carbon-based materials in supercapacitor applications.