The interplay between disease dynamics and vaccinating behaviour has been receiving increasing attention from mathematical modellers, due to recent vaccine scares and other behavioural phenomena. Modellers have developed various coupled "disease-behaviour" models to capture this interplay. Salient challenges to the field include how to reconcile model predictions to empirical observations, and how to incorporate greater realism, both in epidemiology and in terms of how human behaviour is represented. I will give a broad overview of my research from the past 10 years devoted to addressing these challenges, using tools such as dynamical systems, contact network simulations, and model selection approaches. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. The end goal of my research is to develop disease-behaviour models that could help us predict how vaccine scares might unfold and thereby assist mitigation efforts. This talk will be accessible to a general audience.