Cyclodextrins (CDs) are cyclic oligosaccharides of six, seven, or eight glucose units designated as α, β, and γ cyclodextrins respectively. Depicted in the diagram below. Daniel Armstrong is considered the pioneer of micelle and cyclodextrin-based separations. Cyclodextrins are covalently attached to silica by Armstrong process and provide stable CSPs. The primary hydroxyl groups are used to anchor the CD molecules to the modified silica surface. CDs are chiral because of innate chirality of the building blocks, glucose units. In cyclodextrin the glucose units are α-(1,4)- connected. The shape of CD looks like a shortened cone (see the sketch). The inner surface of the cone forms moderately hydrophobic pocket. The width of the CD-cavity is identified with the quantity of glucose units present. In cyclodextrins, secondary hydroxyl groups (OH-2 and - 3) line the upper rim of the cavity, and an essential 6-hydroxyl group is positioned at the lower rim. The hydroxyl group offer chiral binding points, which appear to be fundamental for enantioselectivity. Apolar glyosidic oxygen makes the pit hydrophobic and guarantees inclusion complexing of the hydrophobic moiety of analytes. Interactions between the polar area of an analyte and secondary hydroxyl groups at the mouth of the pit, joined with the hydrophobic connections inside the pit, give a unique two-point fit and lead to enantioselectivity. 
Selectivity of a cyclodextrin phase is dependent on two key factors namely the size and structure of the analyte since it is based on a simple fit-unfit geometric criteria.  An aromatic ring or cycloalkyl ring should be attached near the stereogenic center of the analyte. Substituents at or near the analyte chiral center must be able to interact with the hydroxyl groups at the entrance of the CD cavity through H-bonding. α-Cyclodextrin holds small aromatic molecules, whereas β-cyclodextrin incorporates both naphthyl groups and substituted phenyl groups. The aqueous compatibility of CD and its unique molecular structure make the CD- bonded phase highly suitable for use in chiral HPLC analysis of drugs. One further benefit of CD is that they are generally less expensive than the other CSPs. Some of  the major shortcomings of CD CSPs is that it is limited to compounds that can enter into CD cavity, minor structural changes in analyte leads to unpredictable effect on resolution, often poor efficiency and cannot invert elution order. 
Enantiomers of propranolol, metoprolol, chlorpheniramine, verapamil, hexobarbitaI, methadone and much more drugs have been separated  using immobilized β-cyclodextrin.
Initially natural CDs have been used as the chiral selector. Later, modified cyclodextrin structures have been prepared by derivatizing the secondary hydroxyl groups present on the CD molecule. Incorporation of these additional functional groups may improve the chiral recognition capability by possibly modifying the chiral pocket and creating extra auxiliary interaction site. This approach enabled to expand the range of target chiral analytes that could be separated. A number of chiral pharmaceuticals has been resolved using derivatized CDs including ibuprofen, suprofen, flurbiprofen from NSAID category and b-blockers like metoprolol and atenolol. A brief list of cyclodextrin-based chiral stationary stationary phases available in the market is furnished in the table below.