The emergence of sixth-generation and beyond communication systems is expected to fundamentally transform digital experiences through introducing unparalleled levels of intelligence, efficiency, and connectivity. A promising technology poised to enable this revolutionary vision is a wireless large AI model (WLAM), characterized by its exceptional capabilities in data processing, inference, and decision-making. In light of these remarkable capabilities, this paper provides a comprehensive survey of WLAM, explaining its fundamental principles, diverse applications, critical challenges, and future research opportunities. We begin by introducing the background of WLAM and analyzing the key synergies with wireless networks, emphasizing the mutual benefits. Subsequently, we explore the foundational characteristics of WLAM, delving into their unique relevance in wireless environments. Then, the role of WLAM in optimizing wireless communication systems across various use cases and the reciprocal benefits are systematically investigated. Furthermore, we discuss the integration of WLAM with emerging technologies, highlighting their potential to enable transformative capabilities and breakthroughs in wireless communication. Finally, we thoroughly examine the high-level challenges and discuss pivotal future research directions.

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