► Starches modified by octenyl succinic acid are used extensively in industry. ► Applications include nutritional products and stabilizers. ► Their synthesis, characterization and structure are reviewed. Starches modified with octenyl succinic anhydride (OSA) have been used in a range of industrial applications, particularly as a food additive, for more than half a century. Interest in these products has grown in recent years as a result of new methods and applications becoming available. Due to a combination of OSA's hydrophobic and steric contribution and starch's peculiar highly branched macromolecular structure, these starch derivatives display useful stabilizing, encapsulating, interfacial, thermal, nutritional and rheological properties. We review the synthesis procedures, structural characterization methods and physico-chemical properties, and the influences of the botanical origins and structural parameters of OSA starches on physico-chemical properties. A better understanding of these features has the potential to lead to products with targeted macromolecular structures and optimized properties for specific applications.