The importance of mitochondria in mammalian cells is widely known. Several biochemical reactions and pathways take place within mitochondria: among them, there are those involving the biogenesis of the iron–sulfur (Fe-S) clusters. The latter are evolutionarily conserved, ubiquitous inorganic cofactors, performing a variety of functions, such as electron transport, enzymatic catalysis, DNA maintenance, and gene expression regulation. The synthesis and distribution of Fe-S clusters are strictly controlled cellular processes that involve several mitochondrial proteins that specifically interact each other to form a complex machinery (Iron Sulfur Cluster assembly machinery, ISC machinery hereafter). This machinery ensures the correct assembly of both [2Fe-2S] and [4Fe-4S] clusters and their insertion in the mitochondrial target proteins. The present review provides a structural and molecular overview of the rare diseases associated with the genes encoding for the accessory proteins of the ISC machinery (i.e., GLRX5, ISCA1, ISCA2, IBA57, FDX2, BOLA3, IND1 and NFU1) involved in the assembly and insertion of [4Fe-4S] clusters in mitochondrial proteins. The disease-related missense mutations were mapped on the 3D structures of these accessory proteins or of their protein complexes, and the possible impact that these mutations have on their specific activity/function in the frame of the mitochondrial [4Fe-4S] protein biogenesis is described.