Growing consumption of rare earth elements (REEs) due to their critical roles in various sectors (e.g., healthcare, energy, transportation, and electronics) has gained attention and stimulated research efforts in industry and academic communities. This study provides an overview of the existing REE production and recovery pathways, identifies critical challenges of the current techniques, and highlights opportunities for multidisciplinary research to achieve more effective solutions. A comprehensive classification of REE separation techniques is presented through narrative and systematic literature reviews, including qualitative analysis and classic bibliometric techniques, to assess the usefulness of identified methodologies and approaches. It is found that the top three most explored and mature separation techniques in various phases (solid and liquid) between 2015 and 2020 are leaching, solvent extraction, and plasma; and the top three study fields are chemistry, engineering, and metallurgy. It is further found that the dominant REE separation technique across over 40 fields of research is the use of acids, bases, ionic liquids, and salts for leaching REEs. It is concluded that agromining approach, using hyperaccumulator plants capable of absorbing REEs through their roots and leaves, can be a practical approach for sustainable REEs recovery from secondary sources and end-of-life products, such as electronic devices.