The paper aims at characterising and documenting a fundamental change in how phase transitions were modelled microscopically in the period 1937–1970. At first, physicists took what will be called a naturalistic approach to phase transitions such as the condensation of gases and the Curie point of ferromagnets. Here the purpose was to explain the phenomenon in question, i.e., to show that a model exhibits the same features as the phenomenon. The scope of this approach was broad, as the goal was to account for several aspects of the phenomenon. The employed model should be very realistic and close to the foundational theory, be it classical or quantum mechanics. In the 1960s, the physicists used an alternative approach that they termed a caricature approach. This approach not only required explanation in the above sense but also understanding of the physical phenomenon, i.e. insights into why the phenomenon behaves as it does. The scope was limited to certain aspects of the phenomenon, such as the behaviour near the critical point. The caricature approach used a hierarchy of models, ranging from realistic ones over more simplified models to models that were mere caricatures of the system in question. Hence, the two approaches represent very different orientations when it comes to the purpose and scope, the organisation of the resulting theories, and what models are acceptable.