This chapter introduces the theme of the book: scientific understanding. Science is arguably the most successful product of the human desire for understanding. Reflection on the nature of scientific understanding is an important and exciting project for philosophers of science, as well as for scientists and interested laypeople. As a first illustration of this, the chapter sketches an episode from the history of science in which discussions about understanding played a crucial role: the genesis of quantum mechanics in the 1920s, and the heated debates about the intelligibility of this theory and the related question of whether it can provide understanding. This case shows that standards of intelligibility of scientists can vary strongly. Furthermore, the chapter outlines and defends the way in which this study approaches its subject, differing essentially from mainstream philosophical discussions of explanatory understanding. It concludes with an overview of the contents of the book.