The important nodes in complex networks are the extraordinary nodes which play more significant role than other nodes on the structure and function of the networks. In recent years, the reaserch on indentifying inflential nodes in complex networks has attracted much attention, because of its great theoretical significance as well as the wide range of applications. Aiming at different types of networks and motivated by different problems and applications, researchers have proposed groups of methods. This article systematically reviews more than 30 representative methods which are classified into four categories, and detailedly compares them from the aspects of computing ideas and application scenarios, and futher analyzes the strongness and weakness of each method. On this basis, this article summarizes the existing problems and outlines eight open issues as main challenges in the near future.