Transformers have become a cornerstone of modern artificial intelligence, with remarkable abilities to generalize, adapt, and reason. How do these capabilities arise from training? In this talk, I will present three studies connecting data structure, optimization dynamics, and the mechanisms learned by Transformers. First, I will discuss benign overfitting, showing how attention and value learning interact to produce distinct generalization regimes governed by sample size and signal strength. Second, I will examine in-context learning through task-vector retrieval, explaining how training data organization shapes the extraction of transferable task information. Third, I will study how multi-token prediction helps Transformers learn intermediate computations for planning. Through tractable theoretical models and controlled experiments, these studies offer a statistical learning perspective on how training selects useful representations and computations. I will conclude with future directions toward reliable adaptation and reasoning.