Cyclodextrins, cyclic oligomers of glucose, have been used in pharmaceutical formulations for decades as a result to their biocompatibilities, low toxicities and their abilities to solubilise organic small molecules via inclusion complex formation. The incorporation of cyclodextrins within polymers of numerous types, for use as drug delivery agents, has been explored. Illustrative of the flexibility in polymer chemistry and delivery application that is possible with these materials, two linear cyclodextrin-containing polymers are in preclinical and clinical development for the non-covalent delivery of nucleic acid therapeutics and covalent delivery of a small-molecule drug, respectively. This document provides an overview of the background and progress that has been made with these materials thus far, as well as suggestions for their future development and characterisation.