Formal analyses can be valuable aids to decision-making if their limits are understood. Those limits arise from the two forms of subjectivity found in all analyses: ethical judgments, made when setting the terms of an analysis, and scientific judgments, made when conducting it. As formal analysis has assumed a larger role in policy decisions, awareness of those judgments has grown, as have methods for making them. The present review traces these developments, using examples that illustrate the issues that arise when designing, executing, and interpreting analyses. It concludes with lessons learned from the science and practice of analysis. One common thread in these lessons is the importance of collaborative processes, whereby analysts and decision-makers educate one another about their respective needs and capabilities.