The propensity score is the conditional probability of exposure to a treatment given observed covariates. In a cohort study, matching or stratifying treated and control subjects on a single variable, the propensity score, tends to balance all of the observed covariates; however, unlike random assignment of treatments, the propensity score may not also balance unobserved covariates. The authors review the uses and limitations of propensity scores and provide a brief outline of associated statistical theory. They also present a new result of using propensity scores in case-cohort studies.