Moral learning and decision-making are crucial throughout our lives from infancy to old age. Emerging evidence suggests that there are important differences in how we learn and decide in moral situations, and these may be underpinned by co-occurring changes in the use of model-based values and theory of mind. Here, we review the decision neuroscience literature on moral choices and moral learning considering four key concepts. These concepts are learning and experiencing moral emotions, learning and deciding about other's moral character, moral learning and deciding for others, and moral influence and contagion. We focus on recent behavioural and neuroimaging findings using a value-based decision-making framework, showing how mathematical models of decision-making can be used to determine the computational mechanisms underlying these concepts, uncover their neural correlates, and ultimately provide a mechanistic account of morality across the whole lifespan.