The structure and dynamics of complex networks are central topics of current research. From one side scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, and revealing the unifying principles that are at the basis of many real world networks, with the hope that understanding the structure of a system would lead to a better comprehension of its functions. From the other side, many relevant questions arise when studying complex networks dynamics, such as learning how a large ensemble of systems that interact through a complex wiring topology can behave collectively. I will review the major concepts and results recently accomplished in the study of complex networks, and summarize the relevant applications of these ideas in order to fathom the basic properties of real world networks, that are currently under study in many different disciplines of nonlinear science.