This article uses novel data collected on a weekly basis covering more than 35,000 individuals in the EU to analyze the relationship between trust in various dimensions and COVID-19 vaccine hesitancy. We found that trust in science is negatively correlated, while trust in social media and the use of social media as the main source of information are positively associated with vaccine hesitancy. High trust in social media is found among adults aged 65+, financially distressed and unemployed individuals, and hesitancy is largely explained by conspiracy beliefs among them. Finally, we found that the temporary suspension of the AstraZeneca vaccine in March 2021 significantly increased vaccine hesitancy and especially among people with low trust in science, living in rural areas, females, and financially distressed. Our findings suggest that trust is a key determinant of vaccine hesitancy and that pro-vaccine campaigns could be successfully targeted toward groups at high risk of hesitancy.