Moral learning and decision-making are crucial throughout our lives, from infancy to old age. Emerging evidence suggests that there are important differences in learning and deciding in moral situations, and these are 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. We show how in the earliest years, a sense of self/other distinction is foundational. Sensitivity to intention versus outcome is crucial for several moral concepts and is most similar in our earliest and oldest years. Across all ages, basic shifts in the influence of theory of mind and model-free and model-based learning support moral decision-making. Moving forward, a computational approach to key concepts of morality can help provide a mechanistic account and generate new hypotheses to test across the whole lifespan.