This dissertation argues that the phenomena of presupposition are best understood as arising from certain expressions taking scope over expressions that contain them. According to Barker (2015), an expression takes scope over another containing it "when the larger [(containing)] expression serves as the smaller [(contained)] phrase’s semantic argument." Specifically, it is argued that presupposition projection occurs when a presupposition trigger takes scope over the larger phrase containing it, while presupposition filtering occurs when a presupposition trigger fails to take scope over the larger phrase containing it. Building on the satisfaction account of presupposition put forward by Karttunen (1973) and Heim (1983), this perspective on presupposition is couched within the theory of graded monads, which have recently been proposed, in functional programming languages such as Haskell, as a means to structure the composition of functions and arguments which incur side effects. According to this perspective, presupposition projection is regarded as a side effect to the composition of at-issue meaning. A presupposition trigger is then regarded as taking scope when it incurs side effects. The graded monadic perspective is then applied to a general dynamic semantic account of presupposition and anaphora. Specific topics treated include presupposition projection in conditionals, the complements of propositional attitude verbs, and the scopes of indefinites and distributive quantifiers, like every, as well as null complement anaphora and verb phrase ellipsis. The perspective is shown to offer natural accounts that make good linguistic predictions in each case. One particular advantage of the graded monadic perspective is that it is unsusceptible to the "proviso problem", which has been thought to present a problem for satisfaction accounts of presupposition projection for at least the last two decades. Ultimately, what is offered is a comprehensive, yet simple and modular approach to presupposition in natural language.