Cyclodextrins (CD) are a group of cyclic oligosaccharides with a cavity/specific structure that enables to form inclusion complexes (IC) with a variety of molecules through non-covalent host-guest interactions. By an elegant combination of CD with biocompatible, synthetic and natural polymers, different types of universal drug delivery systems with dynamic/reversible properties have been generated. This review presents the design of nano- and micro-carriers, hydrogels, and fibres based on the polymer/CD supramolecular systems highlighting their possible biomedical applications. Application of the most prominent hydrophobic aliphatic polyesters that exhibit biodegradability, represented by polylactide and polycaprolactone, is described first. Subsequently, particular attention is focused on materials obtained from hydrophilic polyethylene oxide. Moreover, examples are also presented for grafting of CD on polysaccharides. In summary, we show the application of host-guest interactions in multi-component functional biomaterials for controlled drug delivery.