The space-air-ground integrated networks (SAGIN) has emerged as a critical paradigm to address the growing demands for global connectivity and enhanced communication services. This paper gives a thorough review of the strategies and methodologies for resource allocation within SAGIN, focusing on the challenges and solutions within its complex structure. With the advent of technologies such as 6G, the dynamics of resource optimization have become increasingly complex, necessitating innovative approaches for efficient management. We examine the application of mathematical optimization, game theory, artificial intelligence (AI), and dynamic optimization techniques in SAGIN, offering insights into their effectiveness in ensuring optimal resource distribution, minimizing delays, and maximizing network throughput and stability. The survey highlights the significant advances in AI-based methods, particularly deep learning and reinforcement learning, in tackling the inherent challenges of SAGIN resource allocation. Through a critical review of existing literature, this paper categorizes various resource allocation strategies, identifies current research gaps, and discusses potential future directions. Our findings highlight the crucial role of integrated and intelligent resource allocation mechanisms in realizing the full potential of SAGIN for Manuscript