Synthetic iron-sulfur clusters of general formulation [FemSqLi](Z) with core atoms Fe and S and terminal ligands L constitute a family of molecular clusters with remarkably diverse geometrical and electronic structures. Several structure types are also found in proteins. The large majority of research on these clusters has involved elucidation of physical properties. Here, we direct attention to reactivity in the form of cluster conversions in which the FemSq cores of reactants are transformed to new structures, usually of different nuclearity, in overall reactions such as self-assembly and fragment condensation and dissociation. An extensive body of core conversions, many of which have not been recognized as such, are presented including those in biological systems. All structural core types are depicted, and all core conversions are diagrammatically summarized. Clusters containing the cubane-type Fe4S4 core play a central role in conversion chemistry. The core conversion concept tends to reinforce the description of iron-sulfur cores as modular units subject to various covalent bond interactions that lead to different structures.