This chapter focuses on aspects of the philosophy of science, in particular the twentieth century views of Karl Popper and Thomas Kuhn. It briefly covers earlier aspects, including Francis Bacon and William Whewell who highlighted the need for, and influence of, subjective factors in science. In discussing Popper, it considers inductive and deductive reasoning and his falsification approach, while discussion of Kuhn focuses on his view of scientific paradigms, normal science, anomalies and crises, and paradigm shifts and scientific revolutions. It highlights both Popper’s and Kuhn’s views using neuroscience examples, including chemical synaptic transmission, animal electricity and adult neurogenesis. The conclusion is that there is no formal scientific method, no formula for discovery: scientists use, and need to use, a diversity of approaches.