Jean-Pierre Bocquet-Appel formulated the theory of the Neolithic (Agricultural) Demographic Transition, revealing the mechanisms that determine the dynamics of fertility and mortality of populations that adopted the farming way of life. In this way, professor Bocquet-Appel provided the strong theoretical and methodological framework for the paleodemographic research of the process of Neolithization in different times and places in the world. In the last seven years, Bocquet-Appel's ideas inspired and were incorporated into research projects that set out to explore the demographic aspects of the Neolithic transition in the Central Balkans, where little paleodemographic research had been carried out before. The ERC BIRTH project explicitly set out to detect the increase of fertility related to the Neolithic Demographic Transition in the Central Balkans using Bocquet-Appel's theory to deduce hypotheses and build computer simulation models. In this paper I will present a review of what we know and what we do not about the Neolithic Demographic Transition in the Central Balkans and how these results fit into the theory.