"The Cambridge Controversies in Capital Theory discusses the main contributions to the controversy in a series of case studies. It gradually develops a methodological model of idealizations that explains both the process of the debate and the historical ironies surrounding it, revealing that the surrounding confusion was due to the internal dynamics of the debate rather than to ideological differences. Economists were mainly engaged in attempts to solve local problems, often of a highly technical nature. This, plus the use of mathematics, led them to confuse different kinds of idealizations and to drift away from the global problems that were at stake. The main methodological result is a model describing the development of theories by a particular type of generalization: correspondence. The direction in which theories are expanded is ruled by the logical presupposition relationship between the core of a research programme and its corresponding models.