The positron-emitting radionuclide gallium-68 has become increasingly utilised in both preclinical and clinical settings with positron emission tomography (PET). The synthesis of radiochemically pure gallium-68 radiopharmaceuticals relies on careful consideration of the coordination chemistry. The short half-life of 68 min necessitates rapid quantitative radiolabelling (≤10 min). Desirable radiolabelling conditions include near-neutral pH, ambient temperatures, and low chelator concentrations to achieve the desired apparent molar activity. This review presents a broad overview of the requirements of an efficient bifunctional chelator in relation to the aqueous coordination chemistry of gallium. Developments in bifunctional chelator design and application are then presented and grouped according to eight categories of bifunctional chelator: the macrocyclic chelators DOTA and TACN; the acyclic HBED, pyridinecarboxylates, siderophores, tris(hydroxypyridinones), and DTPA; and the mesocyclic diazepines.