Cyclodextrins are glucose macrocycles whose inclusional capabilities towards non-polar solutes can be modulated with the help of other macrostructures. The incorporation of cyclodextrin moieties into larger structures produces five types of new materials: crosslinked networks, functionalized chains, amphiphilic cyclodextrins, polyrotaxanes and nanocomposites. This review presents crosslinking and grafting to prepare covalently-attached cyclodextrins, and applications in the food and pharmaceutical sectors, from an historical point of view. In food science, applications include debittering of juices, retention of aromas and release of preservatives from packaging. In biomedical science, cyclodextrin polymers are applied classically to drug release, and more recently to gene delivery and regenerative medicine. The remarkable points are: 1) epichlorohydrin and diisocyanates have been extensively used as crosslinkers since the 1960s, but during the last two decades more complex cyclodextrin polymeric structures have been designed. 2) The evolution of cyclodextrin polymers matches that of macromolecular materials with regard to complexity, functionality and capabilities. 3) The use of cyclodextrin polymers as sorbents in the food sector came first, but smart packaging is now an active challenge. Cyclodextrins have also been recently used to design treatments against the coronavirus disease 2019 (COVID-19).