Biomining with acidophilic microorganisms has been used at commercial scale for the extraction of metals from various sulfide ores. With metal demand and energy prices on the rise and the concurrent decline in quality and availability of mineral resources, there is an increasing interest in applying biomining technology, in particular for leaching metals from low grade minerals and wastes. However, bioprocessing is often hampered by the presence of inhibitory compounds that originate from complex ores. Synthetic biology could provide tools to improve the tolerance of biomining microbes to various stress factors that are present in biomining environments, which would ultimately increase bioleaching efficiency. This paper reviews the state-of-the-art tools to genetically modify acidophilic biomining microorganisms and the limitations of these tools. The first part of this review discusses resilience pathways that can be engineered in acidophiles to enhance their robustness and tolerance in harsh environments that prevail in bioleaching. The second part of the paper reviews the efforts that have been carried out towards engineering robust microorganisms and developing metabolic modelling tools. Novel synthetic biology tools have the potential to transform the biomining industry and facilitate the extraction of value from ores and wastes that cannot be processed with existing biomining microorganisms.