In this chapter, the focus will be on formal models of hypothetical reasoning , in particular on those concerned with abductive reasoning.In Sect. 10.1 , the chapter offers a brief history of the notion of abduction, starting with an attempt to distinguish it from its closest neighbor, induction. Charles Peirce's original conception of abduction is then presented and followed by an overview of abduction in the cognitive sciences, together with some paradigmatic examples of the kind that will be dealt with in the chapters to follow. Sect. 10.2 presents two main approaches to abduction in philosophy, as argument and as inference to the best explanation (IBE ), something which sets the ground to put forward a general logical taxonomy for abduction. Sect. 10.3 goes deeper into three logic-based classical characterizations of abduction found in the literature, namely as logical inference, as a computational process, and as a process for epistemic change.Hypothetical reasoning is understood here as a type of reasoning to explanations. This type of reasoning covers abductive as well as inductive inferences. As for the latter, in this handbook part, the concern will be limited to enumerative induction and will leave its full presentation to the corresponding chapter (Chap.  11).