A fundamental principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Across the health and social sciences, statistical methods for covariate adjustment are used in pursuit of this principle. Typical methods are matching, regression, and weighting. In this talk, we will examine the connections between these methods through their underlying mathematical programs. We will study their strengths and weaknesses in terms of study design, computational tractability, and statistical efficiency. Overall, we will discuss the role of mathematical optimization for the design and analysis of studies of causal effects.