In abductive reasoning, scientific theories are evaluated on the basis of how well they would explain the available evidence. There are a number of subtly different accounts of this type of reasoning, most of which are inspired by the popular slogan 'Inference to the Best Explanation'. However, these accounts disagree about exactly how to spell out the slogan so as to avoid various problems for abductive reasoning. This Element aims, firstly, to give an opinionated overview both of the many accounts of abductive reasoning that have been proposed and the problems that have motivated them; and, secondly, to critically evaluate these accounts in a way that points towards a systematic view of the nature and purpose of abductive reasoning in science. This title is also available as Open Access on Cambridge Core.