Strategically important elements are those that are vital to advanced manufacturing, low carbon technologies and other growing industries. Ongoing depletion and supply risks to these elements are a critical concern, and thus, recovery of these elements from low-grade ores and brines has generated significant interest worldwide. Among the strategically important elements, this paper focuses on rare earth elements (REEs), the platinum-group metals and lithium due to their wide application in the advanced industrial economics. We critically review the current methods such as precipitation, ion exchange and solvent extraction for extracting these elements from low-grade ores and brines and provide insight into the technical challenges to the practical realisation of metal extraction from these low-grade sources. The challenges include the low concentration of the target elements in brines and inadequate selectivity of the existing methods. This review also critically analyzes the potential applicability of an integrated clean water production and metal extraction process based on conventional pressure-driven membrane and emerging membrane technologies (e.g., membrane distillation). Such a process can first enrich the strategically important elements in solution for their subsequent recovery along with clean water production.