This chapter provides insight into a particular area of enrichment measures, namely student competitions in science - and more concretely the German Science Olympiads - which offer opportunities to challenge and foster students over the entire range of secondary education. It introduces student competitions as effective enrichment measures and deals with the question of what constitutes a 'good' competition. The chapter details the design of the German Science Olympiads, and then focus on research of Olympiads in STEM fields elucidating the scope and limitations of empirical evidence on the effectiveness of competitions in general and the Olympiads in science and mathematics in particular. It focuses on a special kind of competitions, namely those that address individual students in mathematics, science and informatics and elucidate on their contribution to the promotion of gifted students. Competition encourages youth to do things well, better than they would have thought themselves capable of doing.