chapter 1. Introduction -- chapter 2. Transition metal-catalyzed asymmetric epoxidations -- chapter 3. Transition metal-catalyzed asymmetric sulfoxidations -- chapter 4. Miscellaneous transition metal-catalyzed asymmetric oxidations -- chapter 5. Organocatalytic asymmetric oxidations -- chapter 6. Fe- and Mn-based synthetic models of non-heme oygenases : stereospecific C-H oxidations -- chapter 7. Active species and mechanisms of non-heme Fe- and Mn-catalyzed oxidations -- chapter 8. Industrial perspective.