The paper by S.N. Dorogovtsev and J.F.F. Mendes reviews the recent progress in the statistical physics of evolving networks, focusing on the structural properties of random complex networks in various fields such as communications, biology, social sciences, and economics. The authors discuss the emergence of scale-free structures and the "small-world" effect in these networks, where most distances between vertices are short despite the large network sizes. They explore the mechanisms of network growth, including preferential linking, and present models that demonstrate key features of evolving networks. The paper also covers the topological and structural properties of evolving networks, percolation, and the application of these concepts to specific networks in nature, such as citation networks, collaboration networks, and biological networks. Additionally, it discusses the historical background of network studies, the equilibrium and non-equilibrium nature of networks, and the statistical ensemble of growing networks. The authors emphasize the importance of understanding network evolution for various scientific disciplines, including non-equilibrium physics, econophysics, and evolutionary biology.The paper by S.N. Dorogovtsev and J.F.F. Mendes reviews the recent progress in the statistical physics of evolving networks, focusing on the structural properties of random complex networks in various fields such as communications, biology, social sciences, and economics. The authors discuss the emergence of scale-free structures and the "small-world" effect in these networks, where most distances between vertices are short despite the large network sizes. They explore the mechanisms of network growth, including preferential linking, and present models that demonstrate key features of evolving networks. The paper also covers the topological and structural properties of evolving networks, percolation, and the application of these concepts to specific networks in nature, such as citation networks, collaboration networks, and biological networks. Additionally, it discusses the historical background of network studies, the equilibrium and non-equilibrium nature of networks, and the statistical ensemble of growing networks. The authors emphasize the importance of understanding network evolution for various scientific disciplines, including non-equilibrium physics, econophysics, and evolutionary biology.