The Comprehensive Oxford Mathematics and Physics Online School is an innovative large-scale and long-term outreach project within the Department of Physics, University of Oxford. Our mission is to help STEM-talented school students to learn mathematics and physics deeply and systematically through free tuition and mentoring. Students study both subjects. The COMPOS curriculum complements the UK National Curriculum, concentrating on problem-solving skills and understanding at a deeper level. Students receive assignments to solve throughout the academic year. Each assignment includes reading material, links to online lectures and a problem set, one each for both maths and physics. Students' work is marked and returned by their tutor – typically an undergraduate from the Department of Physics at Oxford – who also delivers weekly online tutorials in small groups of students. The assignments and tutorials are complemented by weekly webinars for each year group. In other areas, such as sports or the arts, it is well-established that keen and talented young people need additional training to excel in their chosen field. Musicians can join youth orchestras and choirs, gymnasts can join clubs and compete in tournaments, footballers can join youth academies. COMPOS provides the same out of school enrichment to young people with a strong interest in physics and maths. Thanks to funding by an external private donor Axiom Maths, COMPOS participation is free of charge to UK state school students and is available for a moderate fee to private school and international students. Because all COMPOS activities are online, all that students need to take part is an internet connection and email address.