Bioresources have been gaining popularity due to their abundance, renewability, and recyclability. Nevertheless, given their diverse composition and complex hierarchical structures, these bio-based sources must be carefully processed to effectively extract valuable raw polymeric materials suitable for producing man-made organic fibres. This review will first highlight the most relevant bio-based sources, with a particular focus on promising unconventional biomass sources (terrestrial vegetables, aquatic vegetables, fungi, and insects), as well as agroforestry and industrial biowaste (food, paper/wood, and textile). For each source, typical applications and the biopolymers usually extracted will also be outlined. Furthermore, acknowledging the challenging lignocellulosic structure and composition of these sources, an overview of conventional and emerging pre-treatments and extraction methods, namely physical, chemical, physicochemical, and biological methodologies, will also be presented. Additionally, this review aims to explore the applications of the compounds obtained in the production of man-made organic fibres (MMOFs). A brief description of their evolution and their distinct properties will be described, as well as the most prominent commercial MMOFs currently available. Ultimately, this review concludes with future perspectives concerning the pursuit of greener and sustainable polymeric sources, as well as effective extraction processes. The potential and main challenges of implementing these sources in the production of alternative man-made organic fibres for diverse applications will also be highlighted.