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The development of game agents holds a critical role in advancing towards Artificial General Intelligence (AGI). The progress of LLMs and their multimodal counterparts (MLLMs) offers an unprecedented opportunity to evolve and empower game agents with human-like decision-making capabilities in complex computer game environments. This paper provides a comprehensive overview of LLM-based game agents from a holistic viewpoint. First, we introduce the conceptual architecture of LLM-based game agents, centered around six essential functional components: perception, memory, thinking, role-playing, action, and learning. Second, we survey existing representative LLM-based game agents documented in the literature with respect to methodologies and adaptation agility across six genres of games, including adventure, communication, competition, cooperation, simulation, and crafting & exploration games. Finally, we present an outlook of future research and development directions in this burgeoning field. A curated list of relevant papers is maintained and made accessible at: https://github.com/git-disl/awesome-LLM-game-agent-papers.