Immunization, the most successful public health intervention to date, can only be effective if eligible individuals or their legal representatives have access to vaccines and subsequently comply with their use. Under-vaccination stems from multiple causes: access, affordability, awareness, acceptance and activation. In this paper, we focus on acceptance and, specifically, on factors pertaining to individual or parental compliance, specifically the psychology of judgment and decision making. We describe how heuristics and cognitive biases - a facet of thoughts and feelings - affect vaccination decision making. Additionally, we address when and how social processes play a role and how attitudes towards vaccines might reflect a more general underlying attitude or ideology. The understanding of how decision making, with regards to vaccines occurs, and the role played by heuristics and cognitive biases can help inform more appropriate public health interventions.