The emerging technologies, materials, and industries have a profound and increasing impact on the amount and structure of demand of critical metals. Understanding how technological progress affects the demand for critical metals and minerals is of certain practical significance for the high-quality economic transformation, the low-carbon energy transformation, and the critical minerals security in China. This paper conducted a systematic review of the literature on the relationship between technological progress and critical metal demand, and finds that: As resource security has become an important national demand issue, technological progress and critical metal demand prediction have gradually become a hot spot. However, there are few quantitative studies and lack of systematization in existing literature. And the accuracy of demand forecasting results needs to be further improved due to difficulties in measuring technological progress and data acquisition. In this paper, three micro-influencing mechanisms of technological progress on the demand for critical metals were applied: technological progress—economic growth, industrial structure and substitution and recycle—metal minerals, providing an overall analytical framework for subsequent studies. The focus of follow-up research in this field was proposed, that is, focusing on the coupling problem of low-carbon technology—critical metals and strategic emerging industries—critical metals, solving the measurement problem of technological progress in theoretical and econometric model, and promoting the construction of analytical frameworks for critical metal demand forecasting as technological revolution continues in the new era.