Power is of central importance to competition law. On the one hand, power is related to competitive benefits and harms. On the other hand, power is connected with the methods for observing, measuring and controlling competitive harms. Modern competition law employs the market power conception, which is economic-oriented, incoherent, and fails to show the true nature of the power of businesses. Without an precise understanding of power’s real nature, modern competition law has managed to work for more than a century due to the relatively simple connection and interplay among different power types of traditional businesses. However, the digital economy brings changes to the power and power exercise of businesses, and the power interplay among businesses. For novel power issues raised by the digital economy, conventional competition law tools based on the market power conception frequently fail to address the issues timely, coherently, and effectively. The problems spotted are fixed with considerable difficulties and controversies, e.g. whether competition law rather than other laws should address a problem and which competition law tool(s) to employ. Various attempts have been made to solve the problems but at present, there is still no overarching framework to explain why conventional competition law fails to work properly. This research shows that an important reason is the inaccurate understanding of the nature of the power of businesses. A better understanding of the nature can help identify problems, fill the analysis gaps, better articulate theories of harm, and tackle new challenges. The research examines the philosophical understanding of the nature of power. Based on this, it identifies several prominent power types related to business activities, with attention paid to Internet-based businesses. It also examines competition law’s power and shows that, due to the connection and interplay among different power types, the influence of competition law may go beyond purely economic. Three major challenges raised by the digital economy are employed to show the advantages of the proposed power conception.