This paper presents a comprehensive survey of the current status and opportunities for Large Language Models (LLMs) in strategic reasoning, a complex form of reasoning that involves understanding and predicting the actions of others in multi-agent settings while adjusting strategies accordingly. Strategic reasoning is characterized by its focus on the dynamic and uncertain nature of interactions among agents, requiring the ability to understand the environment and anticipate others' behavior. The paper explores the scope, applications, methodologies, and evaluation metrics related to strategic reasoning with LLMs, highlighting the growing development in this area and the interdisciplinary approaches that enhance their decision-making performance. It aims to systematize and clarify the scattered literature on this subject, emphasizing the importance of strategic reasoning as a critical cognitive ability and offering insights into future research directions and potential improvements. The paper discusses the definition, scenarios, methods, and evaluations of strategic reasoning with LLMs. It defines strategic reasoning as the ability to anticipate and influence the actions of others in competitive or cooperative multi-agent settings. It categorizes strategic reasoning applications into societal simulation, economic simulation, game theory, and gaming. The paper explores various methods to improve LLMs in strategic reasoning, including prompt engineering, modular enhanced agents, theory of mind, and imitation learning with reinforcement learning. It also discusses how to evaluate LLMs' performance in strategic reasoning, including quantitative and qualitative assessments. The paper highlights the challenges and opportunities in applying LLMs to strategic reasoning, emphasizing the need for a systematic review to organize and clarify the differences and connections among existing works. It discusses the importance of strategic reasoning in various domains, including business, policy-making, and gaming, and the potential of LLMs to enhance strategic thinking and decision-making. The paper concludes by emphasizing the need for interdisciplinary collaboration to advance the practical applications of LLMs in strategic reasoning.This paper presents a comprehensive survey of the current status and opportunities for Large Language Models (LLMs) in strategic reasoning, a complex form of reasoning that involves understanding and predicting the actions of others in multi-agent settings while adjusting strategies accordingly. Strategic reasoning is characterized by its focus on the dynamic and uncertain nature of interactions among agents, requiring the ability to understand the environment and anticipate others' behavior. The paper explores the scope, applications, methodologies, and evaluation metrics related to strategic reasoning with LLMs, highlighting the growing development in this area and the interdisciplinary approaches that enhance their decision-making performance. It aims to systematize and clarify the scattered literature on this subject, emphasizing the importance of strategic reasoning as a critical cognitive ability and offering insights into future research directions and potential improvements. The paper discusses the definition, scenarios, methods, and evaluations of strategic reasoning with LLMs. It defines strategic reasoning as the ability to anticipate and influence the actions of others in competitive or cooperative multi-agent settings. It categorizes strategic reasoning applications into societal simulation, economic simulation, game theory, and gaming. The paper explores various methods to improve LLMs in strategic reasoning, including prompt engineering, modular enhanced agents, theory of mind, and imitation learning with reinforcement learning. It also discusses how to evaluate LLMs' performance in strategic reasoning, including quantitative and qualitative assessments. The paper highlights the challenges and opportunities in applying LLMs to strategic reasoning, emphasizing the need for a systematic review to organize and clarify the differences and connections among existing works. It discusses the importance of strategic reasoning in various domains, including business, policy-making, and gaming, and the potential of LLMs to enhance strategic thinking and decision-making. The paper concludes by emphasizing the need for interdisciplinary collaboration to advance the practical applications of LLMs in strategic reasoning.