Two prominent debates in the philosophy of science literature - namely the scientific realism debate and the conventionalism debate - originate in the work of Pierre Duhem and Henri Poincare. This thesis explores problems in the current scientific realism and conventionalism debates and analyses Duhem's and Poincare's roles within these debates. In particulal~ it discusses the problems of underdetermination and theory choice, the problem of constitutivity, the problem of theory change and shows how Duhem and Poincare develop and address them. I present the current scientific realism debate and show Duhem's and Poincare's contribution to it. I evaluate Duhem's and Poincare's arguments against instrumentalism, explain their defence of structuralism and argue that their position is not realist, contrary to what is often assumed. I explore different solutions to the problem of underdetermination and develop objections to them. Following Duhem, I argue that the employment of theoretical virtues does not solve the problem of theory choice on the grounds that they are inconclusive and lead to a further form of underdetermination. Furthermore, I analyse Duhem's notion of 'good sense', which is an attempt at providing a normative non-rule governed account of rationality in theory choice. I address recent interpretations of this concept and develop problems for them. I develop a reading that overcomes the objections to the current readings. I present the evolution of conventionalism, from Poincare's conventions and Hans Reichenbach's constitutive a priori, to Michael Friedman's relativized a priori. I analyse Poincare's arguments for conventionalism and remove some longstanding confusions regarding his view. I discuss Friedman's defence of rationality in scientific revolutions as a solution to the Kuhnian objection of irrationality. Last, I analyse the epistemological status of the relativized a Priori and its intricate relationship with structuralism, which originates in Poincare's philosophy, and argue against current attempts that aim to connect the two theses.