This paper reviews the theoretical analysis of epidemic spreading in complex networks, emphasizing the role of network structure in determining the dynamics of infectious diseases and social contagion processes. It provides a comprehensive overview of the mathematical models, network measures, and theoretical approaches used to study epidemic processes in heterogeneous networks. The paper discusses classical epidemic models such as SIS and SIR, and their extensions, including the SIRS and SEIR models. It also covers the impact of network topology on epidemic behavior, including the role of degree distribution, clustering, and network heterogeneity. The paper highlights the importance of network structure in determining the epidemic threshold and the spread of diseases, and discusses the implications of these findings for public health and social science. It also addresses the challenges of modeling epidemic processes in dynamic, time-varying, and coevolving networks, and the need for more realistic models that incorporate spatial structure, individual heterogeneity, and multiple time scales. The paper concludes with an outlook on future research directions in the study of epidemic processes in complex networks.This paper reviews the theoretical analysis of epidemic spreading in complex networks, emphasizing the role of network structure in determining the dynamics of infectious diseases and social contagion processes. It provides a comprehensive overview of the mathematical models, network measures, and theoretical approaches used to study epidemic processes in heterogeneous networks. The paper discusses classical epidemic models such as SIS and SIR, and their extensions, including the SIRS and SEIR models. It also covers the impact of network topology on epidemic behavior, including the role of degree distribution, clustering, and network heterogeneity. The paper highlights the importance of network structure in determining the epidemic threshold and the spread of diseases, and discusses the implications of these findings for public health and social science. It also addresses the challenges of modeling epidemic processes in dynamic, time-varying, and coevolving networks, and the need for more realistic models that incorporate spatial structure, individual heterogeneity, and multiple time scales. The paper concludes with an outlook on future research directions in the study of epidemic processes in complex networks.