The 1994 structure of a transition-state analogue with AlF4- and GDP complexed to G1 alpha, a small G protein, heralded a new field of research into the structure and mechanism of enzymes that manipulate the transfer of phosphoryl (PO3-) groups. The number of enzyme structures in the PDB containing metal fluorides (MFx) as ligands that imitate either a phosphoryl or a phosphate group was 357 at the end of 2016. They fall into three distinct geometrical classes: 1) Tetrahedral complexes based on BeF3- that mimic ground-state phosphates; 2) octahedral complexes, primarily based on AlF4-, which mimic "in-line" anionic transition states for phosphoryl transfer; and 3) trigonal bipyramidal complexes, represented by MgF3- and putative AlF30 moieties, which mimic the geometry of the transition state. The interpretation of these structures provides a deeper mechanistic understanding into the behavior and manipulation of phosphate monoesters in molecular biology. This Review provides a comprehensive overview of these structures, their uses, and their computational development.