Among numerous synthetic macromolecules, polyurethane in its different forms has proven its sheer dominance and established a reputation as a reliable and trusted material due to its proficiency in terms of superior properties, which include: high mechanical strength and abrasion resistance, good durability, good adhesion, good thermal stability, excellent chemical and weathering resistance. Synthetic polyurethane materials are non-biodegradable, poisonous, and use petrochemical-based raw materials, which are now depleting, leading to a surge in polyurethane production costs. Bio-based polyurethanes (PU) have been synthesized by researchers in recent decades and have mostly overtaken petrochemical-based PU in terms of challenges such as solid pollution, economic effectiveness, and availability of raw materials. Enormous kinds of available bio-renewable sources as predecessors for the production of polyols and isocyanates have been explored for the development of “greener” PU materials; these bio-based polyurethanes have significant potential to be used as future PU products, with a partial or total replacement of petroleum-based polyurethanes, due to increasing concern about the environment, their relatively low cost and biodegradability. This critical review concentrates on the possibilities of renewable sources to be used for polyurethane production and gives a clear perspective on the journey, utilization, and recent advancements in the field of different bio-based polyurethane polymers that have arisen over the last decade.