Low-altitude economy, fine-grained surveying, emergency response, and autonomous exploration are driving Unmanned Aerial Vehicles (UAVs) from passive data-acquisition platforms toward task-executing aerial agents. This capability transition requires UAVs to operate within complex, open 3D environments under six-degree-of-freedom (6DoF) motion, strict size, weight and power (SWaP) limits, partial observations, onboard computation constraints, and safety-critical action requirements. Therefore, the central scientific problem of UAV 3D scene understanding is how a UAV agent can construct, maintain, and use a spatiotemporally coherent and uncertainty-aware 3D scene state to support localization, planning, and safe interaction. Existing surveys mainly categorize the literature according to sensor types, application scenarios, or generic 3D representations, and thus provide limited analysis of how 3D scene understanding supports agent-capability evolution under embodied aerial constraints. To address this gap, we review UAV 3D scene understanding along an agent-capability evolution from offline interpretation to online understanding and predictive reasoning. This perspective highlights the underlying tensions between representation fidelity and onboard deployability, open-vocabulary semantic coverage and calibrated trustworthiness, post-flight static reconstruction and online scene-state maintenance, and predictive reasoning and safety-bounded decision support. Finally, we discuss open challenges in closed-loop data construction, trustworthy scene-state memory, collaborative fusion, sim-to-real transfer, and reliable onboard deployment.