Electricity is a versatile form of energy but suffers from a drawback in that it cannot be stored easily. Supercapacitors are devices that can address this problem. Fabrication of efficient supercapacitors is the need of the hour, which requires an intelligent selection of the electrode materials and electrochemical conditions. In this review, electrochemical studies and synthesis methods of polymer based metal oxide composites, especially polyaniline and polypyrrole, are discussed in detail. Various fabrication methods that are in use for the preparation of the supercapacitor electrodes are evaluated, which gives an idea of the selection of suitable materials for electrochemical applications. The supercapacitance studies of the reported works are also discussed, which help to understand the efficiency and working of different polymer based metal oxide composites for energy applications. Conducting polymers have good capacitance behavior but low cyclic stability. Incorporating metal oxides, graphene, noble metals, MXenes, and carbon nanotubes enhances the capacitance of conducting polymers. Polyaniline based electrodes show comparatively higher capacitance values compared to polypyrrole based electrodes. The types of supercapacitors, the importance of polymers in supercapacitance applications, and the improvement of the polymer substrates by using various materials like metal oxides to enhance the supercapacitance ability are discussed in depth in this review.