Competitions and related activities are an essential part of mathematics education for gifted students. China has been one of the most successful countries in recent decades in the International Mathematical Olympiad. To illustrate the Chinese experience of mathematics competitions, in this paper we first present a historical sketch of Chinese mathematics competitions, then provide a comprehensive description of its pyramidal selection and training systems, including the introduction of main competitions for high school students, some examples of competition problems, and the training of students and tutors. Furthermore, to investigate the influence of mathematics competitions on contestants, an empirical study of 372 former contestants was conducted and is reported. The results showed that most of the contestants majored in mathematics or areas closely related to mathematics. Nearly half of the contestants intended to do mathematics research or work highly related to mathematics. A majority of the contestants held positive attitudes toward their mathematics competition experiences and affirmed the value of these experiences in cultivating personal interests and developing mathematics abilities. Some negative influences of competition experiences on contestants are also identified. Finally, problems existing in the development of Chinese mathematics competitions and future research directions are discussed.