Oxygen reduction reaction (ORR) is one of the fundamental reactions that occur on the cathode of fuel cells. The sluggish kinetics of ORR and the high cost of the conventionally used ORR electrocatalyst mandate extensive research towards the development of inexpensive, high-performance and stable electrocatalysts. Various supported nanostructures of pristine noble metals and its alloys, transition metals/metal oxides (MOs), chalcogens/pnictogens doped metals/MOs, etc. have attracted great attention towards ORR in both acidic and alkaline electrolytes. This review primarily documents the recent advancements and challenges of supported nanomaterials with fascinating properties towards ORR. This study focuses on the use of carbon-based materials as support. The significant factors like size, morphology, hetero-atom doping, defects and interfaces (metal/metal, metal/oxide and metal/hydroxide) that can tailor ORR activity are portrayed elaborately. The electrochemical techniques and parameters that are adopted mainly during data collection and evaluation of ORR are also discussed.