Precision medicine seeks to maximize the quality of health care by individualizing the health-care process to the uniquely evolving health status of each patient. This endeavor spans a broad range of scientific areas including drug discovery, genetics/genomics, health communication, and causal inference, all in support of evidence-based, i.e., data-driven, decision making. Precision medicine is formalized as a treatment regime that comprises a sequence of decision rules, one per decision point, which map up-to-date patient information to a recommended action. The potential actions could be the selection of which drug to use, the selection of dose, the timing of administration, the recommendation of a specific diet or exercise, or other aspects of treatment or care. Statistics research in precision medicine is broadly focused on methodological development for estimation of and inference for treatment regimes that maximize some cumulative clinical outcome. In this review, we provide an overview of this vibrant area of research and present important and emerging challenges.