This chapter maps the reasons why scientific arguments do not lend themselves to straightforward judicial appraisal. The study identifies epistemic, doctrinal, and legitimacy challenges, which generate difficulties in using science in an adjudicatory setting. Epistemic challenges stem from the fact that science and law are both capable of lending cognitive authority to knowledge claims, and these authorities may be in conflict with each other. Doctrinal challenges emerge from the fundamental differences in the ways in which law and science conceive basic concepts and their different levels of tolerance towards probabilistic evidence and uncertainty. Legitimacy challenges entail difficulties for judges to preserve their monopoly over the resolution of disputes and to select the appropriate rationality to justify their reasoning. This chapter also introduces the analytic framework of the book, which is designed to evaluate the varied judicial reactions given to the intrusion of science into the adjudicatory process. It therefore introduces and discusses the framing of disputes, the scientific fact-finding process, the causal inquiry, and the standard of review.