An important motivation for libertarian theories of free will derives from the view that freedom (and moral responsibility) requires the power of origination, the power to act in a way that is not determined by the law-driven causal stream of events that precede the action.  But no plausible libertarian theory can maintain that free actions are completely causally or explanatorily independent of events that precede them: this would make actions chancy, random, and inexplicable--in particular, inexplicable by reasons. For the libertarian, then, prior events and states of affairs--including an agent's circumstances, reasons, and character--must typically function as mere influences on free actions, 'inclining but not necessitating' the agent to act.  This dissertation focuses on the concept of influence--the metaphysical middle ground between determinism and chance--in libertarian accounts of free will and moral responsibility, a concept that, despite its centrality to libertarianism, has not been given a satisfactory explication. One main project of the dissertation is to make significant progress toward an explication of influence; the other main project consists of tracing some of the implications of this explication, especially implications for theories of moral responsibility.  I contribute to an explication of influence in two ways. First, (in the Introduction and Chapters 1 and 2) I identify important sources of influence, distinguish philosophically useful kinds of influence, and clarify salient features and properties of influence. I focus especially on the need to account for the fact that influences vary in strength and hence come in degrees. Second, I raise and develop significant challenges (in Chapters 3 and 4) for extant attempts by non-causal, agent-causal, and event-causal libertarian views to account for influence. Hence, appeals to irreducible teleological relations, objective causal propensities, and relative causal contribution face considerable difficulties, leaving libertarians with substantial metaphysical puzzles. I identify the most promising replies or amendments such views should adopt, though I remain skeptical of their success.  In Chapter 5 I begin the project of tracing the implications of the foregoing chapters by examining the thesis of restrictivism--the view that human freedom is exercised only rarely, under relatively unusual circumstances. I offer numerous refinements to our understanding of the scope and nature of our overall freedom, and thereby help to frame the final chapter in which I take up questions about moral responsibility.  The main conclusion defended in the final chapter is that one's degree of moral responsibility or desert for an act or consequence ought to be a function, partly, of the kinds and strengths of influences on it. Against arguments to the contrary, I defend the view that moral responsibility for an act is mitigated to the degree to which it is, in certain ways, influenced. Moreover, I argue that actual human agents typically are subject to influences of a kind and strength that does in fact tend to sharply diminish their moral responsibility--more than seems to be presupposed by most libertarians. Hence, even mere influence can pose a threat to freedom and moral responsibility.