Background: Since vaccination is the decisive factor for controlling the COVID-19 pandemic, it is important to understand the process of vaccination success which is not well understood on a global level. The study is the first to judge the now completed "first wave" of the vaccination efforts. The analysis is very relevant for the understanding why and where the vaccination process observed got stuck by the end of 2021. Methods: Using data from 118 countries globally and weighted least squared and survival analysis, we identify a variety of factors playing crucial roles, including the availability of vaccines, pandemic pressures, economic strength measured by Gross Domestic Product (GDP), educational development, and political regimes. Results: Examining the speed of vaccinations across countries until the Fall of 2021 when the global process got stuck, we find that initially authoritarian countries are slow in the vaccination process, while education is most relevant for scaling up the campaign, and the economic strength of the economies drives them to higher vaccination rates. In comparison to North and Middle America, European and Asian countries vaccinated initially fast for 5% and 10% vaccination rate thresholds, but became rather slow reaching the 30% vaccination level and above. The findings are robust to various applied estimation methods and model specifications. Conclusions: Democratic countries are much faster than authoritarian countries in their vaccination campaigns when controlling for other factors. This finding suggests that the quality of government and the political environment play a key role in popular support for government policies and programs. However, despite the early success of their vaccination campaigns, the democratic country group has been confronted with strong concerns of vaccine reluctance among their vast populations, indicating the two most potent variables explaining the speed of the COVID-19 vaccination campaign are education and economic conditions.