The paradigm of Earth Observation analysis is shifting from static deep learning models to autonomous agentic AI. Although recent vision foundation models and multimodal large language models advance representation learning, they often lack the sequential planning and active tool orchestration required for complex geospatial workflows. This survey presents the first comprehensive review of agentic AI in remote sensing. We introduce a unified taxonomy distinguishing between single-agent copilots and multi-agent systems while analyzing architectural foundations such as planning mechanisms, retrieval-augmented generation, and memory structures. Furthermore, we review emerging benchmarks that move the evaluation from pixel-level accuracy to trajectory-aware reasoning correctness. By critically examining limitations in grounding, safety, and orchestration, this work outlines a strategic roadmap for the development of robust, autonomous geospatial intelligence.