The swift evolution of Large-scale Models (LMs), either language-focused or multi-modal, has garnered extensive attention in both academy and industry. But despite the surge in interest in this rapidly evolving area, there are scarce systematic reviews on their capabilities and potential in distinct impactful scenarios. This paper endeavours to help bridge this gap, offering a thorough examination of the current landscape of LM usage in regards to complex game playing scenarios and the challenges still open. Here, we seek to systematically review the existing architectures of LM-based Agents (LMAs) for games and summarize their commonalities, challenges, and any other insights. Furthermore, we present our perspective on promising future research avenues for the advancement of LMs in games. We hope to assist researchers in gaining a clear understanding of the field and to generate more interest in this highly impactful research direction. A corresponding resource, continuously updated, can be found in our GitHub repository.