 Philosophical issues related to scientific discovery arise about the nature of human creativity, specifically about whether the “eureka moment” can be analyzed and about whether there are rules (algorithms, guidelines, or heuristics) according to which such a novel insight can be brought about. Philosophical issues also arise about the analysis and evaluation of heuristics, about the characteristics of hypotheses worthy of articulation and testing, and, on the meta-level, about the nature and scope of philosophical analysis itself. This essay describes the emergence and development of the philosophical problem of scientific discovery and surveys different philosophical approaches to understanding scientific discovery. In doing so, it also illuminates the meta-philosophical problems surrounding the debates, and, incidentally, the changing nature of philosophy of science.