The 'philosophy of science' debates concerning epistemology and methodology are critically appraised: the logical positivist view is shown to have fatal weaknesses; 'tolerant criticism' is proposed as prescriptive methodology; Lakatos' framework is argued to be very beneficial descriptively; the biblical-Christian worldview is recommended as a foundation for science. Various approaches to issues in economic methodology are critically reviewed. A version of sophisticated falsificationism is proposed for prescription. The subject-matter of economics implies that testability in economics is not straightfoward and must be complemented with understanding; and that predictive accuracy is an inappropriate criterion for theory-choice in economics. The Lakatos framework of 'research programmes' (RP's) is used to analyse the Keynesian-monetarist-new classical controversy. Awareness of the hard-cores of these particular RP's enables one to understand the inability of empirical tests to resolve the controversy. Both the Keynesian and monetarist RP's are shown to have been initially progressive, then turning degenerate, whilst the new classical school is a budding RP. It is argued that the truth/falsity of hard-core statements should be much more closely examined; that to have critical outsiders in the controversy is legitimate and necessary, and that moral value-judgments are a significant factor in this controversy. A methodological critique of Rational Expectations (RE) reveals very little support for RE on either a priori or instrumentalist grounds. The success of RE is considerably explained by its inclusion in the hard-core of a monetarist RP approaching degeneracy, transforming the latter into theoretically progressive new classicism. Conclusions are drawn concerning the factors influencing the choice between research programmes.