Economists pay much attention to the impact of competition on innovation. This paper concludes the theory evolution and the development of empirical research in this field, and makes deep discussion about the setting and measurement of index. In the theory evolution part, this paper reviewed three major hypotheses on impact of competition to innovation and recent studies on the impact of competition on enterprise innovation. In the part of index setting and measurement, it illustrates about the measurement of creation and market competition. In the part of empirical research development, this essay not only pays attention to the competition under the creation effect inside the industry, but also focuses on it among the industry, i.e. the influence of service industry and the competition of upstream industry to the downstream manufacturing, and also makes review of the research findings about China.