Agentic AI systems introduce a security surface that is qualitatively different from that of stateless LLMs. They persist memory, invoke external tools, coordinate with peer agents, and operate across sessions, allowing attacks to emerge not only at the prompt interface but also through architectural state, delegated authority, and long-horizon interactions. Existing security taxonomies, however, primarily organize threats by attack type, such as prompt injection or jailbreaking, and therefore obscure where in the agentic stack a threat arises and over what timescale it manifests. We propose the Layered Attack Surface Model (\lasm), a structural taxonomy for agentic AI security. \lasm decomposes the agentic stack into seven layers -- Foundation, Cognitive, Memory, Tool Execution, Multi-Agent Coordination, Ecosystem, and Governance -- and augments them with a four-class temporality axis covering instantaneous, session-persistent, cross-session cumulative, and sub-session-stack threats. We use this 7$\times$4 framework to analyze 116 papers from 2021--2026. The resulting map reveals that the upper layers of the agentic stack remain sharply under-explored, especially for long-horizon and stack-propagating threats; multiple documented attack regions have no corresponding defenses; and current benchmarks provide no coverage for cross-session or sub-session-stack failure modes. We further derive a cross-layer defense taxonomy, defense recipes for canonical attack classes, and a dependency DAG that separates near-term engineering gaps from fundamental research challenges. We release the per-paper coding, robustness scripts, and a reference Agent Bill of Materials schema to support reproducible analysis.