Matched sampling, where the researcher first finds for each exposed unit (e.g., a smoker) a non-exposed unit (e.g., a never-smoker) who looks exactly like the exposed unit except for the exposure, and then compares outcomes (e.g., lung cancer rates) for the matched samples of units, is an intuitive method for inferring the causal effects of exposure versus non-exposure on the collection of units. Although intuitive, very little formal statistical work was done exploring the utility of matched sampling for rigorous causal inference until the late 1960s, starting with Cochran (1968). The statistical work from that time to the early 2000s is summarized in a text, Rubin (2006), but since that time there has been an explosion of work on such matching, primarily in social science. Some of these newer methods depend critically on modern computing (e.g., Diamond and Sekhon, 2013) and thus on machine learning ideas, but some methods are a century old. This series of lectures will: review this body of literature; identify critical issues with some of the intuitive, but mathematically misguided, recent efforts; and focus on new methods using recent ideas. When evaluating procedures, we will consider the combination of model-based adjustments on the matched samples, an idea that dates from the early 1970s.