Complex systems which are composed of many interacting entities can be represented, analyzed and better understood using a network representation, where the entities are represented by nodes and the interactions by links. In recent years it was realized that the topology of many real networks is very different from that of the classical graph theory. In particular, while classical graphs were assumed to be homogeneous with every node having a typical number of links (degree) real networks are usually heterogeneous (e.g., the Internet) with nodes having very different degrees. Thus, many properties of networks were not understood and many open questions were asked. The finding of the new topology led, in recent years, to the emergence of a active field of complex networks where new suitable theories and approaches are developed. I will discuss these developments as well as many recent applications, such as robustness, effective immunization strategies and optimal transport in real world networks. References: [1] Transport in weighted networks: partition into superhighways and roads Z. Wu, L.A. Braunstein, S. Havlin, H.E. Stanley Phys. Rev. Lett. 96, 148702 (2006) [2] Limited path percolation in complex networks E. Lopez, R. Parshani, R. Cohen, S. Carmi, S. Havlin Phys. Rev. Lett. 99, 188701 (2007) [3] A model of Internet topology using k-shell decomposition S. Carmi, S. Havlin, S. Kirkpatrick, Y. Shavitt, E. Shir PNAS 104, 11150 (2007) [4] Climate networks around the globe are significantly affected by El Nino K. Yamasaki, A. Gozolchiani, S. Havlin Phys. Rev. Lett. 100, 228501 (2008) [5] Finding a Better Immunization Strategy Y. Chen, G. Paul, S. Havlin, F. Liljeros, and H. E. Stanley Phys. Rev. Lett. 101, 058701 (2008)