The goal of a well-controlled study is to remove unwanted variation when estimating the causal effect of the intervention of interest. Experiments conducted in the basic sciences frequently achieve this goal using experimental controls, such as "negative'' and "positive'' controls, which are measurements designed to detect systematic sources of unwanted variation. Here, we introduce clear, mathematically precise definitions of experimental controls using potential outcomes. Our definitions provide a unifying statistical framework for fundamental concepts of experimental design from the biological and other basic sciences. We discuss experimental controls as tools for researchers to wield in designing experiments and detecting potential design flaws, including using controls to diagnose unintended factors that influence the outcome of interest, assess measurement error, and identify important subpopulations.