This review correlates lanthanide-ion affinities with the polarizability of the donor atoms on immobilized ligands to gain an insight into the design of lanthanide-selective polymer-supported reagents. Comparison With the affinities for actinide ions clarifies the correlation. Polymers with different ligands are classified into four categories, based on an increasing order of donor atom polarizability: oxygen, oxygen and nitrogen, nitrogen, and sulfur. Hard-soft acid-base theory is an important determinant of ion-ligand affinities. Additional factors that affect complexation levels include counterion coordination to the metal, protonation of the ligand, and hydration. Selectivity for the lanthanide ions may be engineered into polymer-supported reagents by introducing phosphonic acid ligands.