Agentic Satellite-Augmented Low-Altitude Economy and Terrestrial Networks: A Survey on Generative Approaches

The development of satellite-augmented low-altitude economy and terrestrial networks (SLAETNs) demands intelligent and autonomous systems that can operate reliably across heterogeneous, dynamic, and mission-critical environments. To address these challenges, this article surveys the state-of-the-art literature on enabling agentic artificial intelligence (AI), that is, artificial agents capable of perceiving, reasoning, and acting, through the application of generative AI (GAI) and large language models (LLMs) in SLAETNs. We begin by introducing the architecture and characteristics of SLAETNs, analyzing the challenges that arise in integrating satellite, aerial, and terrestrial components. Then, we present a model-driven foundation by systematically reviewing five major categories of generative models: variational autoencoders (VAEs), generative adversarial networks (GANs), generative diffusion models (GDMs), transformer-based models (TBMs), and LLMs. Moreover, we discuss critical deployment strategies and propose a conceptual framework for deploying agentic AI in SLAETNs. Building on this foundation, we examine how these models empower agentic functions across three domains: communication enhancement, security and privacy protection, and intelligent satellite tasks. Moreover, we present a comprehensive guide to open-source frameworks, datasets, and simulation platforms, and deliver a case study on agentic network optimization in SLAETN scenarios. Finally, we outline key future directions for building scalable, adaptive, and trustworthy generative agents in SLAETNs. This survey aims to provide a unified understanding and actionable reference for advancing agentic AI in next-generation networks.