The interest in natural fibres and biopolymers for developing bio-composites has greatly increased in recent years, motivated by the need to reduce the environmental impact of traditional synthetic, fossil fuel-derived materials. However, several limitations associated with the use of natural fibres and polymers should be addressed if they are to be seriously considered mainstream fibre reinforcements. These include poor compatibility of natural fibres with polymer matrices, variability, high moisture absorption, and flammability. Various surface treatments have been studied to tackle these drawbacks, such as alkalisation, silane treatment, acetylation, plasma treatment, and polydopamine coating. This review paper considers the classification, properties, and limitations of natural fibres and biopolymers in the context of bio-composite materials. An overview of recent advancements and enhancement strategies to overcome such limitations will also be discussed, with a focus on mechanical performance, moisture absorption behaviour, and flammability of composites. The limitations of natural fibres, biopolymers, and their bio-composites should be carefully addressed to enable the widespread use of bio-composites in various applications, including electronics, automotive, and construction.