Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand and, thus, warrant a causal interpretation of the estimated effect. In this article, we discuss and compare the identifying assumptions of quasi-experiments using causal graphs. The increasing complexity of the causal graphs as one switches from an RCT to RD, IV, or PS designs reveals that the assumptions become stronger as the researcher's control over treatment selection diminishes. We introduce limiting graphs for the RD design and conditional graphs for the latent subgroups of compliers, always takers, and never takers of the IV design, and argue that the PS is a collider that offsets confounding bias via collider bias. [For a related paper, see ED567736.]