This survey provides an overview of statistical network models and their applications across various fields, including social sciences, computer science, physics, and biology. It begins with a historical overview of network modeling approaches, highlighting key contributions from early researchers such as Simmel, Wolff, Moreno, and Erdős-Rényi. The survey then delves into static and dynamic network models, discussing models like the Erdős-Rényi-Gilbert random graph, exchangeable graph models, $p_1$ and $p_2$ models for social networks, exponential random graph models (ERGMs), and blockmodels. It also covers dynamic models for longitudinal data, including preferential attachment, small-world, and Markov models. The survey emphasizes the interpretation of parameters and estimation methods, and concludes with a discussion of open problems and challenges in network modeling. The authors aim to provide a comprehensive yet concise guide to the major schools of thought and approaches in network modeling, while also identifying gaps in the current literature.This survey provides an overview of statistical network models and their applications across various fields, including social sciences, computer science, physics, and biology. It begins with a historical overview of network modeling approaches, highlighting key contributions from early researchers such as Simmel, Wolff, Moreno, and Erdős-Rényi. The survey then delves into static and dynamic network models, discussing models like the Erdős-Rényi-Gilbert random graph, exchangeable graph models, $p_1$ and $p_2$ models for social networks, exponential random graph models (ERGMs), and blockmodels. It also covers dynamic models for longitudinal data, including preferential attachment, small-world, and Markov models. The survey emphasizes the interpretation of parameters and estimation methods, and concludes with a discussion of open problems and challenges in network modeling. The authors aim to provide a comprehensive yet concise guide to the major schools of thought and approaches in network modeling, while also identifying gaps in the current literature.