Many contemporary historians debate and ponder whether modern universities represent a unique creation of the high Middle Ages in Europe, or a simple evolution of schools and academies of classical antiquity. Policymakers, though, could also benefit from addressing this question because in order to find appropriate solutions to reforming universities, one needs to be aware of their history, the paths they have taken, and the traditions that determined their developmental logic. This article aims to do just that. Based on a historical analysis, the authors offer a concept of the university as a symbiosis of liberal education, the medieval guild, and natural sciences. This model allows us to identify the most important missions and functions of universities, and thus to define the idea or identity of the "European university" behind all the diversity of existing institutions. We propose to use this model as the foundation upon which the integration of various European educational systems can take place most successfully.