As a cofactor, iron–sulfur (Fe–S) cluster binds to proteins or enzymes that play important roles in various important biological processes, including DNA synthesis and repair, mitochondrial function, gene transcription and translation. In mammals, the core components involved in Fe–S cluster biosynthesis are considered to include the scaffold protein ISCU, cysteine desulfurase NFS1 and its accessory proteins ISD11 and ACP, and frataxin (FXN). Proteins involved in Fe–S cluster transfer have been found to include HSC20/HSPA9, as chaperone system, and Fe–S cluster carriers. The biosynthesis and transfer of Fe–S clusters to Fe–S recipients require fine-tune regulation. Recently, significant progress has been made in the structure and mechanism of mitochondrial Fe–S biosynthesis and transfer. Based on, especially, the development of DNA sequencing technology, bioinformatics, and gene editing technology, diseases caused by mutations of Fe–S cluster-related genes have been revealed in recent years, promoting the rapid development in the field of Fe–S and human health. This review focuses on the function of genes involved in Fe–S cluster biosynthesis and transfer and on the diseases caused by the mutations of the related genes. Finally, some questions we are facing are raised, new hypotheses presented, and the perspectives discussed.