This article reviews the statistical mechanics of complex networks, focusing on their topology and dynamics. It discusses the empirical data that motivated the study of complex networks, and covers key models and analytical tools, including random graphs, small-world and scale-free networks, as well as the interplay between topology and robustness against failures and attacks. The paper begins with an introduction to complex networks, then reviews empirical results from various real-world networks, such as the World-Wide Web, Internet, movie actor collaboration network, science collaboration graph, and others. It then discusses random graph theory, including the Erdős-Rényi model, subgraphs, graph evolution, degree distribution, connectedness, clustering coefficient, and graph spectra. The paper also covers percolation theory, generalized random graphs, small-world networks, the scale-free model, evolving networks, error and attack tolerance, and future outlook. The study highlights the three main concepts in complex networks: small path length, clustering, and scale-free degree distribution, which have led to the development of three main modeling paradigms: random graphs, small-world models, and scale-free models. The paper concludes with a discussion of the implications of these findings for understanding complex systems and the future directions of research in this field.This article reviews the statistical mechanics of complex networks, focusing on their topology and dynamics. It discusses the empirical data that motivated the study of complex networks, and covers key models and analytical tools, including random graphs, small-world and scale-free networks, as well as the interplay between topology and robustness against failures and attacks. The paper begins with an introduction to complex networks, then reviews empirical results from various real-world networks, such as the World-Wide Web, Internet, movie actor collaboration network, science collaboration graph, and others. It then discusses random graph theory, including the Erdős-Rényi model, subgraphs, graph evolution, degree distribution, connectedness, clustering coefficient, and graph spectra. The paper also covers percolation theory, generalized random graphs, small-world networks, the scale-free model, evolving networks, error and attack tolerance, and future outlook. The study highlights the three main concepts in complex networks: small path length, clustering, and scale-free degree distribution, which have led to the development of three main modeling paradigms: random graphs, small-world models, and scale-free models. The paper concludes with a discussion of the implications of these findings for understanding complex systems and the future directions of research in this field.