The paper discusses the challenges and future directions of wireless systems, particularly in the context of supporting advanced applications like digital twins (DTs) and holographic teleportation. It highlights that current 6G and AI-native wireless systems, while promising, still rely on conventional AI tools that struggle with complex, non-trivial scenarios and evolving quality-of-experience requirements. To address these limitations, the authors propose a fundamental revision of AI-native wireless systems, equipping them with common sense to transform them into artificial general intelligence (AGI)-native systems. The proposed AGI-native wireless systems are designed to acquire common sense through cognitive abilities such as perception, analogy, and reasoning, enabling them to generalize and handle unforeseen scenarios effectively. The system is structured around three main components: a perception module, a world model, and an action-planning component. These components collectively enable four pillars of common sense: dealing with unforeseen scenarios, capturing intuitive physics, performing analogical reasoning, and filling in missing elements. The paper also discusses the integration of brain-inspired methods like integrated information theory and hierarchical abstractions to enhance planning and decision-making. Finally, the authors explore three use cases related to human users and autonomous agents, including analogical reasoning for DTs, synchronized and resilient experiences for cognitive avatars, and brain-level metaverse experiences exemplified by holographic teleportation. The paper concludes with recommendations to further develop AGI-native systems and serves as a roadmap for the next generation of wireless networks beyond 6G.The paper discusses the challenges and future directions of wireless systems, particularly in the context of supporting advanced applications like digital twins (DTs) and holographic teleportation. It highlights that current 6G and AI-native wireless systems, while promising, still rely on conventional AI tools that struggle with complex, non-trivial scenarios and evolving quality-of-experience requirements. To address these limitations, the authors propose a fundamental revision of AI-native wireless systems, equipping them with common sense to transform them into artificial general intelligence (AGI)-native systems. The proposed AGI-native wireless systems are designed to acquire common sense through cognitive abilities such as perception, analogy, and reasoning, enabling them to generalize and handle unforeseen scenarios effectively. The system is structured around three main components: a perception module, a world model, and an action-planning component. These components collectively enable four pillars of common sense: dealing with unforeseen scenarios, capturing intuitive physics, performing analogical reasoning, and filling in missing elements. The paper also discusses the integration of brain-inspired methods like integrated information theory and hierarchical abstractions to enhance planning and decision-making. Finally, the authors explore three use cases related to human users and autonomous agents, including analogical reasoning for DTs, synchronized and resilient experiences for cognitive avatars, and brain-level metaverse experiences exemplified by holographic teleportation. The paper concludes with recommendations to further develop AGI-native systems and serves as a roadmap for the next generation of wireless networks beyond 6G.