The concept of immobilizing ligands onto cross-linked polymer supports is presented as an evolution of a concept that begins with ion exchange resins and evolves into ion-selective polymers, polymer-supported catalysts, and the general area of polymer-supported reagents. Each of the four categories of polymers is defined by a set of major variables {electrostatic attraction (for ion exchange resins); steric, geometric, and electronic factors (for ion-selective polymers); attracting and orienting reactants, and stabilizing the transition state (for polymer-supported catalysts); and binding reactants with weak or strong forces (for polymer-supported reagents)} and of minor variables {pH, concentration, competing ions, counterions, ionic strength, hydrophilic/hydrophobic interactions, hydration energies, and polymer crosslink level}. The rational design of each category will require identifying the relationships between major and minor variables and applying the principles inherent to complexity science will be an important focus of future research. (c) 2017 Society of Chemical Industry