Batteries are the main component of many electrical systems, and due to the elevated consumption of electric vehicles and portable electronic devices, they are the dominant and most rapidly growing energy storage technology. Consequently, they are set to play a crucial role in meeting the goal of cutting greenhouse gas emissions to achieve more sustainable societies. In this critical report, a rational basic-to-advanced compilation study of the effectiveness, techno-feasibility, and sustainability aspects of innovative greener manufacturing technologies and processes that deliver each battery component (anodes, cathodes, electrolytes, and separators) is accomplished, aiming to improve battery safety and the circularity of end-products. Special attention is given to biomass-derived anode materials and bio-based separators utilization that indicates excellent prospects considering green chemistry, greener binders, and energy storage applications. To fully reach this potential, one of the most promising ways to achieve sustainable batteries involves biomass-based electrodes and non-flammable and non-toxic electrolytes used in lithium-ion batteries and other chemistries, where the potential of a greener approach is highly beneficial, and challenges are addressed. The crucial obstacles related to the successful fabrication of greener batteries and potential future research directions are highlighted. Bridging the gap between fundamental and experimental research will provide critical insights and explore the potential of greener batteries as one of the frontrunners in the uptake of sustainability and value-added products in the battery markets of the future.