The Berezinski-Kosterlitz-Thouless (BKT) and the superconductor-insulator transition (SIT) are paradigmatic examples of a thermal and a quantum phase transition in two dimensions. For thin superconducting films, it is still open how these two types transitions are connected in the limit of strong localization. Here we combine AC- and DC-transport measurements for the same devices and follow the evolution of the BKT-transition all the way to the superconductor-insulator transition (SIT). The universal BTK characteristics are maintained over the full range of superconductivity. The observed dependence on disorder is correctly described by mean-field theories until presumed quantum phase fluctuations set in close to the SIT. In the latter regime, our data are consistent with quantum critical behavior. Our results reconcile the long-standing puzzle of the BKT-transition in 2D superconductors and the origin of the SIT.