The past few decades have witnessed renewed interest and research efforts on the part of the scientific community. After spending decades to disassemble nature, focusing the attention on its components, scientists have shifted their attention on complex networks. These basic structures constitute a wide range of systems in nature and society, but their design is irregular, evolves dynamically over time and their components can fit in a large multiplicity of alternative ways. Nevertheless, the most recent studies of networks have made remarkable progresses by investigating some critical issues of structure and dynamics, thereby improving the understanding of the topology and the growth processes of complex networks. From an economic point of view, networks are especially interesting because they can be considered as a problem of allocation of a critical resource, information, under multiple constraints. They can also be viewed as forms of poliarchies that reproduce, for many aspects, the market paradigm, with surprising properties of self-organization and resilience, which go much beyond the characteristics that are generally attributed to general equilibrium structures. In this paper we first address the major results achieved in the study of complex network and then focus our attention on two specific, highly dynamic and complex networks: Internet and the World Wide Web.