The processes for the selective oxidation of olefins have long been among the most useful tools for day-to-day organic synthesis. Herein, the focus is on the asymmetric-epoxidation (AE) and asymmetric-dihydroxylation (AD) reactions developed by Sharpless and co-workers. The reactions have a wide scope, are simple to run, and involve readily available starting materials. Ligand-accelerated catalysis is crucial to these reactions and might be the agent for uncovering more catalytic processes. In addition to the selectivity benefits of catalysis, the phenomenon of turnover (amplification) raises its potential impact. The author and his co-workers developed small, highly enantioselective catalysts that were unfettered by the “lock-and-key” selectivity of Natures enzymes, and tolerant of substrates throughout the entire range of olefin substitution patterns.