The increasing global environmental concerns and awareness of renewable green resources is continuously expanding the demand for eco-friendly, sustainable and biodegradable natural fibre reinforced composites (NFRCs). Natural fibres already occupy an important place in the composite industry due to their excellent physicochemical and mechanical properties. Natural fibres are biodegradable, biocompatible, eco-friendly and created from renewable resources. Therefore, they are extensively used in place of expensive and non-renewable synthetic fibres, such as glass fibre, carbon fibre and aramid fibre, in many applications. Additionally, the NFRCs are used in automobile, aerospace, personal protective clothing, sports and medical industries as alternatives to the petroleum-based materials. To that end, in the last few decades numerous studies have been carried out on the natural fibre reinforced composites to address the problems associated with the reinforcement fibres, polymer matrix materials and composite fabrication techniques in particular. There are still some drawbacks to the natural fibre reinforced composites (NFRCs)—for example, poor interfacial adhesion between the fibre and the polymer matrix, and poor mechanical properties of the NFRCs due to the hydrophilic nature of the natural fibres. An up-to-date holistic review facilitates a clear understanding of the behaviour of the composites along with the constituent materials. This article intends to review the research carried out on the natural fibre reinforced composites over the last few decades. Furthermore, up-to-date encyclopaedic information about the properties of the NFRCs, major challenges and potential measures to overcome those challenges along with their prospective applications have been exclusively illustrated in this review work. Natural fibres are created from plant, animal and mineral-based sources. The plant-based cellulosic natural fibres are more economical than those of the animal-based fibres. Besides, these pose no health issues, unlike mineral-based fibres. Hence, in this review, the NFRCs fabricated with the plant-based cellulosic fibres are the main focus.