Both the structure and function of many complex systems can be described in terms of networks consisting of nodes and links between them. The nodes can be either individual components or sub-systems and the strength of the connections between these can be fixed or variable. In recent years, there has been a great deal of interest in structural aspects of networks and the exploration of dynamics on these topologies is now rapidly expanding. The talk will consist of two parts, the first of which will focus on our recent work on a statistical mechanism for generating networks. This new model has some distinct advantages over the well-studied and widely used preferential attachment scheme and provides a unified framework for generating a wide variety of degree distributions with other attributes seen in real-world network data. The second part of the talk will deal with network applications such as the issue of vulnerability of complex networks to targeted attacks as well as discussing some preliminary results on spatio-temporal dynamics and resulting patterns on networks.