Given the current highest demand in history for raw materials, there is a growing demand for the recovery of key metals from secondary sources, in order to prevent metal depletion and to reduce the risk of toxic discharges into the environment. This paper focuses on the current nature-based solutions (i.e., biomining and bioleaching) applied to resource recovery (metals) from solid matrices. Biomining exploits the potential of microorganisms to facilitate the extraction and recovery of metals from a wide range of waste materials as an interesting alternative, replacing primary raw materials with secondary material resources (thus improving metal recycling rates in the context of the circular economy). Special attention was paid to the analysis of metal biomining from a process sustainability perspective. In this regard, several supporting tools (e.g., life cycle assessment, LCA), developed to assist decision-makers in the complex process of assessing and scaling-up remediation projects (including biomining), were discussed. The application of LCA in biomining is still evolving, and requires comprehensive case studies to improve the methodological approach. This review outlines the fact that few studies have focused on demonstrating the environmental performance of the biomining process. Also, further studies should be performed to promote the commercial opportunities of biomining, which can be used to recover and recycle metals from solid matrices and for site remediation. Despite some important disadvantages (poor process kinetics; metal toxicity), biomining is considered to be a cleaner approach than conventional mining processes. However, implementing it on a large scale requires improvements in regulatory issues and public acceptance.