This paper reviews the use of game theory tools to study the operation and design of modern power grids. The contribution of this work is to summarize the literature to highlight the versatile solution capability of game theory by focusing on the interconnected objectives of energy trading and energy management. This review was conducted with a focus on various applications in energy systems, including general energy markets, micro grids (MGs), virtual power plants (VPP), electric vehicles (EVs), and smart homes, and explores how game theory can summarize the solutions for pricing, bidding, demand side management, and resource optimization. A key finding is the suitability of game theory for modeling decentralized energy systems where strategic incentives can lead to outcomes that benefit both individuals and society. It also discusses the limitations, challenges, and potential benefits of game theory in complex power systems. This study provides researchers and policy makers with a comprehensive overview of current research and insights into the potential of game theory to shape the future of energy systems.