The agricultural and livestock sectors of Latin America produce a large number of residues that could be converted into energy through bioenergy production processes. However, the bioenergy sector still faces several limitations across the region, including fragmented logistics systems, weak coordination among institutions, and limited integration of environmental, digital, and compliance-related performance indicators. This review systematically analyses residue-based bioenergy value chains in Latin America between 2015 and 2025 using the PRISMA methodology to evaluate selected peer-reviewed studies and regional reports indexed in Scopus, ScienceDirect, SpringerLink, and IEEE Xplore, and institutional repositories. The final synthesis included 37 studies and institutional contributions, which were further disaggregated into 208 country–residue observations for the regional and feedstock distribution analysis. The review identified three main research gap categories: the limited integration of collection and logistics systems, the insufficient treatment of uncertainty, circularity, and traceability within optimization models, and the weak incorporation of governance and institutional coordination into bioenergy value-chain design. The analysis includes biogas, biomethane and related residue-based systems, with attention to supply-chain optimization, policy alignment, methane mitigation metrics, and traceability requirements. Results indicate that although technologies such as biomass pretreatment, process intensification, and upgrading processes continue to improve conversion performance, most studies still focus mainly on technical feasibility and biomass potential. Less attention is given to governance constraints, uncertainty analysis, and monitoring systems capable of supporting regulatory compliance. This research introduced the Sustainable Bioenergy Chain Management Framework (SBCMF) to respond to these limitations and bring together different aspects of bioenergy management within one analytical structure. The framework combines supply-chain optimization under spatial and temporal constraints, circular economy valorisation, methane-related climate performance, and digital traceability, while also linking techno-economic system design with governance and monitoring requirements. In this way, it can help support the development of more transparent and low-carbon bioenergy systems across Latin America.