<p>This paper develops a new framework for thinking about how understanding comes in degrees and what it means for an agent—human or artificial—to “understand” the world. We argue that understanding a target involves appreciating its modal structure, and that growth in understanding proceeds both vertically (penetrating deeper into the levels of the target) and horizontally (appreciating more of each level’s elements). We identify four levels of understanding: mapping a target’s elements (Level 1), grasping their powers and capacities (Level 2), identifying difference makers (Level 3), and apprehending necessitators (Level 4). We then apply this framework to the ongoing debate about whether AI systems possess world models, clarifying what is required for such models to be vehicles of understanding. While we remain neutral on whether current AI systems genuinely understand, we argue that our framework illuminates key issues and charts a path for future research.</p>