Vaccine hesitancy—defined by the World Health Organization (WHO) as a “delay in acceptance or refusal of vaccines despite availability of vaccination services”—is not a recent phenomenon. Historical records indicate that vaccine hesitancy existed by the 18th century in Europe and even resulted in violent riots. The drivers of vaccine hesitancy have evolved over the last 200 years but not, perhaps, as much as one might expect. More problematic are the means by which concerns over vaccine hesitancy are communicated by a new landscape of digital communication, generating what has been described as an “infodemic” in which an overabundance of information—both factual and misinformation—contributes to hesitancy. In this review, we discuss the background and current drivers of vaccine hesitancy and the evidence base for strategies to combat this. We highlight the important role the allergy/immunology community could have in working to mitigate vaccine hesitancy, particularly with respect to the current coronavirus disease 2019 (COVID-19) pandemic.