This survey examines game theory-based approaches and optimization techniques for electric vehicle (EV) charging systems. We analyze various frameworks, including coalition, Stackelberg, and non-cooperative game theory, alongside nature-inspired optimization algorithms like particle swarm optimization and genetic algorithms. The survey explores how these frameworks address key challenges such as optimal station placement, dynamic pricing, and grid load balancing. A key finding is that while individual methods offer robust theoretical models, hybrid approaches that combine game theory with optimization algorithms consistently outperform single-method solutions in practical applications. We conclude by identifying critical research gaps, including the need for highly scalable solutions to manage large EV fleets and the seamless integration of renewable energy sources into the charging infrastructure, highlighting these as crucial directions for future research.