Conceptual modelling in software engineering is dominated by the implicit semantics of UML, some other OMG products, and a bunch of related modelling tools. Although other alternatives to modelling are seen in academic circles, industry is dominated by this single approach. With no room to improve and no freedom to experiment, stagnation is guaranteed. The paper claims that a technology-free, purely theoretical analysis of models and modelling is necessary in order to find what real models are about, what the real modelling mechanisms behind software engineering are, and what kind of modelling infrastructure should serve as a foundation for future modelling technologies.