The goal of this research was to provide an overview of the role of trust in determining COVID-19 vaccine acceptance. Trust proved to be a key issue in all the strategic phases of the pandemic, a decisive element for the success of the worldwide vaccination campaign. By introducing a comprehensive systematic review of the state-of-the-art (N = 43), we intend to shed light on the various forms of trust that have been considered and how these relate to citizens' vaccine acceptance. The analysis shows that trust has been used extensively, with particular reference to the COVID-19 vaccine, governments, manufacturers, healthcare systems, and science. A more in-depth analysis has also allowed us to evaluate the role that these factors have had and the social phenomena in which they have been decisive. Most notably, we proved that, in the different contributions, trust in the COVID-19 vaccine has a strong correlation with vaccine acceptance (R = 0.78, p < 0.01). Overall, vaccine acceptance emerges as a complex phenomenon that needs to be understood through the strictly interlaced relations of trust in the various factors coming into play. Besides clarifying what happened in previous years, the considerations included in this work also represent an important and useful interpretative framework to help public institutions and the healthcare system in the future.