Rare earth elements (REEs) are becoming increasingly important in the development of modern and green energy technologies with the demand for REEs predicted to grow in the foreseeable future. The importance of REEs lies in their unique physiochemical properties, which cannot be reproduced using other elements. REEs are sourced through mining, with global exploration of additional commercially viable mining sites still ongoing. However, there is a growing need for recycling of REEs due to the current supply of REEs not matching the growing demand, the environmental impact of REE mining and processing (the so-called “balance problem”), and the generation of large volumes of harmful electronic waste (e-waste). Industrial REE processing is mainly carried out by hydrometallurgy processes, particularly solvent extraction (SX) and ion exchange (IX) technologies. However, these methods have a significant environmental impact due to their intensive use of harmful and nonsustainable reagents. This Review highlights the development of approaches involving polymer-based extracting materials for REE manufacturing as more sustainable alternatives to current industrial REE processing methods. These materials include supported liquid membranes (SLMs), solvent impregnated resins (SIRs), macro and micro capsules, polymer inclusion membranes (PIMs), and micro polymer inclusion beads (μPIBs). Polymer-based extracting materials have the advantage of more economical regent usage while applying the same extractants used in commercial SX, enabling applications analogous to the current industrial process. These materials can be fabricated by a variety of methods in a diverse range of physical formats, with the advantages and disadvantages of each material type described and discussed in this Review along with their applications to REE processing, including e-waste recycling and mineral processing.