The boom in technological advances in recent decades has led to increased demand for rare earth elements (REEs) (also known as rare earth metals) across various industries with wide-ranging industrial applications, including in the clean energy sector, but with some environmental, economic, and social footprint concerns. This paper reviews the complexities of the production, consumption, and reuse or recovery of REEs, presenting current trends in terms of potentials and challenges associated with this. This paper in particular focuses on the supply, demand, and (environmental and economic) sustainability of REEs, as a subset of critical raw materials. It does so via a critical stocktaking of key discussions and debates in the field over the past 15 years up until now, through a thematic analysis of the published and gray (policy) literature with a grounded theory approach. The paper finds that carefully balanced lifecycle sustainability assessments are needed for assessing the respective dimensions of the extraction, processing, and reuse or recovery methods for different types of REE sources and supplies to meet current and future demands. It furthermore diagnoses the need for taking into account some shifts and substitutions among REEs also for reasons of cost and locational supplies for the security of supply. Finally, the paper provides some overall policy recommendations for addressing current problems, with a conceptual framing of the UN Sustainable Development Goals.