At present, complex network has quickly formed a cross-disciplinary discipline across many fields, and its relevant theories have been applied to many fields. To understand the research status of complex networks, starting from the definition and statistical characteristics perspectives of complex network, we introduce the basic concept of complex network, then enumerate several typical complex networks model, and on this basis, we set up the improved models and discuss their advantages and disadvantages. Focusing two aspects of structural characteristics of complex networks and network dynamics, we further analyze the current status of research on complex networks, and the research achievements of recent years are listed. Finally, the future research direction of complex network is summarized and forecasted.