This paper presents a causal framework for supervised domain adaptation, addressing how models can effectively generalize from source domains with abundant data to a target domain with limited examples. The authors propose structure-informed procedures that utilize knowledge of the underlying causal structure and domain discrepancies to transport inferences, achieving faster adaptation rates than traditional methods. They also introduce structure-agnostic algorithms that perform nearly as well, even without explicit structural information. The paper extends these concepts to sequential prediction tasks and outlines a computationally efficient two-stage learning procedure for agnostic adaptation, supported by theoretical guarantees and empirical evaluations.