This survey provides an overview of statistical network models, focusing on both static and dynamic approaches. It discusses the historical development of network modeling, key models, and their applications across various fields such as social sciences, computer science, physics, and biology. The survey highlights the importance of network analysis in understanding complex relationships and interactions, and it addresses challenges in modeling network data, including the need for robust statistical methods and the interpretation of parameters. The survey begins with an introduction to the motivations for network analysis and presents several examples of datasets used in network studies. These include social networks, email communication, protein interaction networks, and health-related studies. The text then delves into static network models, such as the Erdős-Rényi-Gilbert model, exchangeable graph models, and exponential random graph models. These models are used to describe the structure and properties of networks, with a focus on how they capture the main elements of actual networks. Dynamic network models are also discussed, including models for longitudinal data and evolving networks. The survey emphasizes the importance of understanding the mechanisms that govern changes in network structures over time. It also addresses issues in network modeling, such as the need for efficient computation, the use of networks for sampling, and the application of machine learning techniques to network analysis. The survey concludes with a summary of the key findings and challenges in network modeling, emphasizing the need for further research in this area. It also highlights the importance of statistical methods in analyzing network data and the potential for future developments in this field. The survey serves as a comprehensive overview of the current state of network modeling and its applications, providing a foundation for further research and exploration in this rapidly evolving area of study.This survey provides an overview of statistical network models, focusing on both static and dynamic approaches. It discusses the historical development of network modeling, key models, and their applications across various fields such as social sciences, computer science, physics, and biology. The survey highlights the importance of network analysis in understanding complex relationships and interactions, and it addresses challenges in modeling network data, including the need for robust statistical methods and the interpretation of parameters. The survey begins with an introduction to the motivations for network analysis and presents several examples of datasets used in network studies. These include social networks, email communication, protein interaction networks, and health-related studies. The text then delves into static network models, such as the Erdős-Rényi-Gilbert model, exchangeable graph models, and exponential random graph models. These models are used to describe the structure and properties of networks, with a focus on how they capture the main elements of actual networks. Dynamic network models are also discussed, including models for longitudinal data and evolving networks. The survey emphasizes the importance of understanding the mechanisms that govern changes in network structures over time. It also addresses issues in network modeling, such as the need for efficient computation, the use of networks for sampling, and the application of machine learning techniques to network analysis. The survey concludes with a summary of the key findings and challenges in network modeling, emphasizing the need for further research in this area. It also highlights the importance of statistical methods in analyzing network data and the potential for future developments in this field. The survey serves as a comprehensive overview of the current state of network modeling and its applications, providing a foundation for further research and exploration in this rapidly evolving area of study.