After a person has become stuck on a problem, they sometimes achieve a clear and sudden solution through insight--the so-called Aha! experience. Because of its distinctive experience, the origins and characteristics of insight have received considerable attention historically in psychological research. However, despite considerable progress in characterizing insight, the underlying mechanisms remain mysterious. We argue that research on insight could be greatly advanced by supplementing traditional insight research, which depends on a few complex problems, with paradigms common in other domains of cognitive science. We describe a large set of mini-insight problems to which multiple methods can be applied, together with subjective reports to identify insight problem-solving. Behavioral priming and neuroimaging methods are providing evidence about what, where, and how neural activity occurs during insight. Such evidence constrains theories of component processes, and will help to demystify insight.