In a seminar with the title "Deduction and Induction in the Sciences", it is intriguing to ask the following questions: (i) Is there a third type of inference besides deduction and induction? (ii) Does this third type of inference play a significant role within scientific inquiry? A positive answer to both of these questions was advocated by Charles S. Peirce throughout his career, even though his opinions changed in important ways during the fifty years between 1865 and 1914. Peirce called the third kind of inference "hypothesis", "abduction", or "retroduction".¹ In this paper, I shall follow Peirce's steps in discussing abduction by analyzing its logical form (Sections 1–3), its role in science (Section 4), and the grounds of its validity (Sections 5–6). We shall see that Peirce's discussion is more insightful than many recent attempts to analyze abductive inference. Still, recently some progress has been made in the treatment of abduction within the Bayesian theory of epistemic probability (Section 6) and truth-approximation (Section 7). The results of this work support the view of scientific realism: abduction or inference to the best explanation (IBE), combined with empirical and experimental testing of scientific theories, is the best method of seeking informative truths in science (Section 8).