Scientific realists and non-realists disagree over the reach of scientific knowledge: does it extend beyond the observational realm. Intuitions about abductive inferences are at the heart of many realist positions, but are brought into question by the non-realists' contention that theories are underdetermined by data, and the alleged circularity of realist attempts to show that such inferences are reliable. Some realists have tried to circumvent this problem by constructing methodological arguments for realism: if realism is embedded in scientific practice, the realist's picture of science might provide the best explanation of scientific success. Some non-realists reply by again pointing to the circularity of this strategy, which relies, again, on an abductive inference. Others deny that scientists do adopt realist stances. A methodological realist position is constructed: realist constraints on the acceptance and pursuit of theories-for instance requirements of intertheoretic coherence, and the avoidance of ad hoc explanation-have often contributed to progress in science. The position is immune to non-realist worries about the circularity of realist arguments, for it is a thesis about how science is practised, not the kind of knowledge it provides. The argument is pursued within a diachronic account of theory appraisal: Imre Lakatos' methodology of scientific research programmes (MSRP) examines the principles that govern the construction of theories, and provides criteria-achievement of progress-for the appraisal of research programmes. Although Lakatos may have seen these selection criteria, when fulfilled, as symptoms of something else-the fulfilment in the theory's development of some ideal of scientific honesty-achievement of Lakatosian progress can Serve as an end in itself. The realist methods mentioned in the last paragraph are then appraised as means to this end. Since the position has a methodological formulation and background, it is applied as a historical thesis to case studies in line with Lakatos' metamethodology. These comprise two explanatory forays into history: the consistency of Bohr's 1913 model of the atom, and the construction by Heisenberg and Schrodinger of the two original formulations of quantum mechanics. There follows one contemporary application: the construction of explanations in quantum chemistry using approximate models of molecules.