The next generation Web technologies (in a broader sense than World Wide Web), as one of the ultimate goals in Web Intelligence (WI) research, will enable humans to go beyond the existing functionalities of online information search and knowledge queries and to gain from the Web practical wisdoms of living, working, and playing. This is a fundamental paradigm shift towards the so-called Wisdom Web, and presents new challenges as well as opportunities to computer scientists and practitioners. In this keynote talk, I will highlight one of the most important manifestations of such technologies, namely, computing with communities of autonomous entities. These communities establish and maintain a vast collection of socially or scientifically functional networks. The dynamic interaction among autonomous entities, such as information exchanges, experience sharing, and service transactions following some predefined protocols, will lead to the dynamic formation, reformation, and consolidation of such networks. As a result, networks of common practice or shared markets will emerge. The dynamic interaction among autonomous entities is a complex one, in which various types of interesting emergent behavior can be induced and observed. Not only should the dynamics of formation and growth of the networks be modeled, but more importantly the dynamics of network functions with respect to certain purpose-directed criteria should be characterized. Such dynamically emergent behavior will depend on the local interaction policies adopted. Knowledge gained from these studies will be invaluable in that it allows us to determine the structural characteristics, computational efficiency, and functional optimality of self-organizing networks, and provides us with insights into the role of local interaction policies. In the talk, I will discuss the important research questions and methodologies underlying the studies of network behavior and structures, which cover the modeling of network dynamics, the characterization of network structures, and the design and optimization of network autonomy.