The unintended memorization of training data in large language models (LLMs) raises important privacy and reliability concerns, particularly in medical applications. In this talk, I will present recent advances from our group in evaluating and controlling LLM memorization, including input-dependent soft prompts for measuring memorization and model-editing methods for inducing or suppressing it. I will then discuss structural memorization in biomedical language models, focusing on PubMed-scale scientific text. Beyond memorizing individual passages, models may retain higher-order structures such as relationships among biomedical concepts, entities, and scientific knowledge. I will discuss how such structural memorization can be characterized and its implications for reliable and trustworthy medical AI.