In this thesis I motivate and develop a Hybrid Theory of Induction (HTI), and I explore some of its virtues and implications. The HTI is a hybrid second-order model of inductive support. It is a hybrid model of inductive support because it holds that two ingredients play a necessary role in understanding inductive support: rules and facts. It is a second-order model of inductive support because it is a model within which first-order models of inductive support (i.e. logics of induction) can fit. In chapter 1 I argue that we need both rules and facts to play a role in a successful account of inductive support. Rules of induction accurately describe relations of inductive support when they are warranted; facts do the warranting work. I call this type of warrant "factual warrant''. The resulting account is both functional and accurate, it helps us make sense of how different rules of induction can coexist and it allows us to resolve some current debates in induction. For the purposes of chapter 1 I adopt an existing binary account of factual warrant. In chapter 2 I develop a Graded account of Factual Warrant (GFW), according to which factual warrant comes in degrees. I integrate the GFW in the HTI. I then show that the GFW illuminates the connection between factual warrant and inductive support, and it can successfully account for the role of idealisations and theory in our understanding of inductive support. In chapter 3 I argue that the HTI is also useful for agents, since it can provide methodological guidance to ensure strong inferences and conceptual guidance to assess the strength of our inferences. Finally, in chapter 4, I explore Bayesian inductive logics from the perspective of the HTI. This analysis brings to light the central role that probability models play in Bayesian inductive logics, offering a logical underpinning for some recent suggestions in Bayesian epistemology. Furthermore, throughout this thesis I analyse in detail three rules of induction from the perspective of the HTI: enumerative induction in chapter 2, causal inference in chapter 3 and Bayesian inductive logics in chapter 4. These analyses illustrate how the HTI can help us think more clearly about rules of induction, offering new tools to tackle existing challenges.