This paper introduces a systematic framework for **agentic AI adaptation**, categorizing research into four distinct paradigms based on whether the **agent** or its **tools** are being optimized. **Agent adaptation** involves updating core models using either **tool-execution signals** for causal feedback or **agent-output signals** for holistic task performance. In contrast, **tool adaptation** focuses on refining external modules, either as **agent-agnostic** components or through **agent-supervised** learning where a fixed model guides tool development. By analyzing these strategies, the authors highlight a transition from **monolithic systems** toward **modular ecosystems** that favor data efficiency and architectural flexibility. The survey concludes by identifying future opportunities in **co-adaptation** and **continual learning** to build more robust, self-evolving autonomous systems.