Vaccination has been the most effective approach in the fight against COVID-19 pandemic. More than half of the world's population has been vaccinated and sufficient data is available to analyze the impact of COVID-19 vaccines around the globe. In this paper, we present a correlation analysis between administered vaccine doses and COVID-19 cases/deaths in Europe. The correlation analysis is performed considering different types of vaccinations, different age groups and different COVID-19 variants (including the prevalent Delta and Omicron variants). We present a detailed analysis for 30 European countries giving various insights such as efficacy of six different vaccines, effect of vaccinating different age groups and how the correlation evolves as different COVID-19 variants emerge. [ABSTRACT FROM AUTHOR]