This paper presents a comprehensive analytical review of contemporary mathematical models of information influence and control in social networks, emphasizing the integration of agent-level factors such as trust, reputation, decision-making, and action execution. We introduce extensions to classical models, including the DeGroot model, by incorporating these critical components to more accurately reflect social interactions. Special attention is given to control strategies and the application of game-theoretic methods for analyzing interactions among controlling entities. We apply these models and methods to real-world social network data, including analyses of ideological preferences and public opinions on health measures during the COVID-19 pandemic. Our approach provides new perspectives for future research in social process modeling and offers insights for designing effective strategies for information influence and control.