Cyclodextrins are cage-shaped molecules having the remarkable ability to trap smaller compounds, and have thus led to applications in many disciplines such as medicine to increase the bioavailability of hydrophobic drugs. This historical review summarizes the outstanding contribution of the late Professor Benito Casu to cyclodextrin research and, more generally, to the chemistry and biochemistry of linear and cyclic oligosaccharides, polysaccharides, glycosaminoglycans, and heparin. Professor Casu was the first to elucidate the structure and conformations of cyclodextrins by infrared spectroscopy and proton nuclear magnetic resonance (NMR). In particular, he showed that trapped compounds induced a shift of H peaks in NMR due to the shielding effect of cyclodextrins. He also demonstrated that the d-glucopyranose cyclodextrin units are in the C-1 chair conformation by analyzing α-cyclodextrin by NMR in dimethylsulfoxide-d6.