The notion of 'anomaly' has persisted for over 2,000 years, but its precise meaning and significance remains unclear. This dissertation analyzes the importance of scientific anomaly both for the philosophy of science and for ethical decision-making that draws on scientific information. In the philosophy of science, it develops a novel account of anomaly. It first provides a conceptual framework for describing anomalies and critically evaluates previous descriptions by Karl Popper, Thomas Kuhn, Imre Lakatos, Larry Laudan, and Lindley Darden. Using the anomalous contemporary biological phenomenon known as 'chemical hormesis' (i.e., beneficial effects from low doses of toxins) as a case study, the dissertation argues for a novel account that emphasizes three features of anomaly. Namely, researchers 'characterize' anomalies in multiple ways, scientists use multiple strategies to 'confirm' them, and anomalies interact with novel hypotheses in an ongoing, dialectical fashion. The dissertation argues that this account is significant because it facilitates increased understanding of scientific discovery and of the role that value judgments play in science. The ethical component of the dissertation analyzes the ethical ramifications both of the hormesis case in particular and of policy-relevant anomalies in general. Concerning the hormesis case, it argues that current evidence for the anomaly does not provide adequate reason to alter regulatory policy. In the process, the dissertation contributes to metaethics by developing a novel formulation of the naturalistic fallacy and by clarifying its relation to the is/ought distinction. Regarding scientific anomaly in general, the dissertation argues that researchers and policymakers have an ethical responsibility to take reasonable steps to identify, reveal, and provide representative information about all major, plausible characterizations of scientific anomalies to the public or its representatives. This study suggests three rules of thumb (namely, analysis of anomalies via analytic-deliberative processes, elimination and disclosure of conflicts of interest, and research-ethics education on scientists' social responsibilities) to help researchers meet their ethical responsibilities with respect to anomalies. The dissertation as a whole illustrates how the philosophy of science can contribute not only to greater understanding of scientific reasoning but also to ethical insights for using scientific knowledge.