The issue of trust in science has come to the fore in recent years. I focus on vaccines, first looking at what is known about trust in vaccines and then concentrating on whether what science education teaches about vaccines can be trusted. I present an argument to connect the phenomenon of vaccine hesitancy to the issue of trust and then argue for what an education about vaccines in school science might look like that takes seriously the notion of respect for students, including students who hold views about vaccination with which science teachers might disagree. Trust in others (people and institutions) varies greatly, both between countries and within countries, and depends on the characteristics of both trustor and trustee, and there are great differences in the extent to which people trust vaccines. However, it is a mistake to think that people who do not trust vaccines are simply ill-informed. There are a range of reasons for rejecting what is often an unexamined narrative about vaccines, namely that vaccines are always desirable. Many people come from communities that have sound reasons for being suspicious of what they are told by governments, business and the medical establishment. COVID-19 and earlier reactions to vaccination health scares show how important high-quality education about vaccines is. Much of that education can take place out of school, but the foundations are laid in school. Vaccine rejection and hesitancy have major global public health implications. Good quality vaccine education should help students understand about relevant biology and the nature of science; it should also be respectful of all students, including those who come from families that reject vaccines or are hesitant about them.