Large language models (LLMs) are often portrayed as merely imitating linguistic patterns without genuine understanding. We argue that recent findings in mechanistic interpretability (MI), the emerging field probing the inner workings of LLMs, render this picture increasingly untenable--but only once those findings are integrated within a theoretical account of understanding. We propose a tiered framework for thinking about understanding in LLMs and use it to synthesize the most relevant findings to date. The framework distinguishes three hierarchical varieties of understanding, each tied to a corresponding level of computational organization: conceptual understanding emerges when a model forms "features" as directions in latent space, learning connections between diverse manifestations of a single entity or property; state-of-the-world understanding emerges when a model learns contingent factual connections between features and dynamically tracks changes in the world; principled understanding emerges when a model ceases to rely on memorized facts and discovers a compact "circuit" connecting these facts. Across these tiers, MI uncovers internal organizations that can underwrite understanding-like unification. However, these also diverge from human cognition in their parallel exploitation of heterogeneous mechanisms. Fusing philosophical theory with mechanistic evidence thus allows us to transcend binary debates over whether AI understands, paving the way for a comparative, mechanistically grounded epistemology that explores how AI understanding aligns with--and diverges from--our own.