I will explore two directions. First, I will explore algorithmic foundations for model stealing of language models.  Model stealing, where a learner tries to recover an unknown model through query access, is a critical problem in machine learning. Here, I will aim to build a theoretical foundation for designing model stealing algorithms.  Second, I will introduce Hamiltonian learning, a central computational task towards understanding and benchmarking quantum systems.  I will highlight how the lens of learning theory plays a key role in identifying and circumventing previous barriers and allows us to give efficient algorithms in settings that were previously conjectured to be intractable.