The literature on methods in and beyond political science has focused a great deal on how to conduct research, but largely neglected the question of why a particular study should be undertaken. It suggests that the rationale for new research is that (1) it fills a ‘gap’; (2) addresses an important real-world problem; and/or (3) is methodologically rigorous. We argue that these justifications are both individually and collectively insufficient. Instead, we propose that a research puzzle is more useful for clarifying the nature and importance of a contribution to existing research. This lecture explores and clarifies what research puzzles are, and introduces a method for constructing such puzzles out of the vague ideas and questions that often trigger a research process.