Abstract: In recent years the discovery of small-world effects and scale-free properties of real-life networks has attracted a much interest among physicists. Which are the most important statistical characteristics for complex networks that are known from regular networks and random networks? What is the ultimate goal of the study of complex networks? Are physical processes sensitive to the topological structure of networks? What are the reason and meaning for physicists to enter the research field of complex networks? What are the directions for future research? In this paper we concentrate on the above questions and present a general overview of complex networks.