Fibers come from natural and fossil resources and are an essential commodity widely used by textile industries. Considering current supply and future demands, the repurposing of agricultural residues into fibers is an eco-friendly, attractive option that might mitigate environmental pollution. In this review, we have summarized multiple alternate secondary sources for fiber production, with a case study using banana plant residual biomass, a common agricultural waste in many developing countries. Specifically, in this review we have compared the different processing methods, e.g., chemical, mechanical, or biological methods, for repurposing agricultural residual biomass (including banana waste) into fibers. The development and analysis of an integrated biorefinery approach is needed to promote the fiber production from various agro-residual biomasses within the framework of circular bioeconomic concepts.