Directions from which this discussion of radical criminology departs are identified and discussed briefly, including that direction which seeks to defend mainstream criminology and that direction which from the position of orthodox Marxism objects to the very concept and practice of a Marxist or radical criminology. Some of the major points of misunderstanding that surround the differences between Marxist and positivist methodologies as they have been applied to the study of crime and its control are considered. Attention then turns to examination of the excesses of radical criminology--its metafunctionalism, its instrumentalism, and its romanticism of illegality-that have grown out of attempts to defeat conventional criminological wisdom from within. These weaknesses are explored with the intention of discovering how they have prevented radical criminology from taking a genuinely critical path. Some of the differences in methodological perspective between old and new criminologists are then addressed to suggest not only why Marxist analysis is so widely misunderstood, but also why it seems to represent such an unscientific approach to the investigation of crime in capitalist society. The methodological issues analyzed are the two schools' (positivist and Marxist) viewpoints on facts and values, the meaning of objectivity, plausibility versus proof, the dialectical method and its limits, and quantiphobia. Final remarks aim to show the increasing necessity of empirical research in critical criminology and the increasing ineffectiveness of traditional criminology. Nine notes and 47 references are provided. For related documents, see NCJ 70048-54 and 70056-62.