In 2019, the World Health Organization (WHO) named "Vaccine Hesitancy" one of the top 10 threats to global health. Shortly afterward, the COVID-19 pandemic emerged as the world's predominant health concern. COVID-19 vaccines of several types have been developed, tested, and partially deployed with remarkable speed; vaccines are now the primary control measure and hope for a return to normalcy. However, hesitancy concerning these vaccines, along with resistance to masking and other control measures, remains a substantial obstacle. The previous waves of vaccine hesitancy that led to the WHO threat designation, together with recent COVID-19 experience, provide a window for viewing new forms of social amplification of risk (SAR). Not surprisingly, vaccines provide fertile ground for questions, anxieties, concerns, and rumors. These appear in new globalized hyperconnected communications landscapes and in the context of complex human (social, economic, and political) systems that exhibit evolving concerns about vaccines and authorities. We look at drivers, impacts, and implications for vaccine initiatives in several recent historical examples and in the current efforts with COVID-19 vaccination. Findings and insights were drawn from the Vaccine Confidence Project's decade long monitoring of media and social media and its related research efforts. The trends in vaccine confidence and resistance have implications for updating the social amplification of risk framework (SARF); in turn, SARF has practical implications for guiding efforts to alleviate vaccine hesitancy and to mitigate harms from intentional and unintentional vaccine scares.