The increasing demand for Li-ion batteries for electric vehicles sheds light upon the Co supply chain. The metal is crucial to the cathode of these batteries, and the leading global producer is the D.R. Congo (70%). For this reason, it is considered critical/strategic due to the risk of interruption of supply in the short and medium term. Due to the increasing consumption for the transportation market, the batteries might be considered a secondary source of Co. The outstanding amount of spent batteries makes them to a core of urban mining warranting special attention. Greener technologies for Co recovery are necessary to achieve sustainable development. As a result of these sourcing challenges, this study is devoted to reviewing the techniques for Co recovery, such as acid leaching (inorganic and organic), separation (solvent extraction, ion exchange resins, and precipitation), and emerging technologies—ionic liquids, deep eutectic solvent, supercritical fluids, nanotechnology, and biohydrometallurgy. A dearth of research in emerging technologies for Co recovery from Li-ion batteries is discussed throughout the manuscript within a broader overview. The study is strictly connected to the Sustainability Development Goals (SDG) number 7, 8, 9, and 12.