The neural circuitry involved in moral decisions has been studied since the early days of cognitive neuroscience, mainly using moral dilemma. However, the neurocomputational mechanisms describing how the human brain makes moral decisions and learns in various moral contexts are only starting to be established. Here we review recent results from an emerging field using model-based fMRI, which describes moral choices at a mechanistic level. These findings unify the field of moral decision making, extend a conceptual framework previously developed for value-based decision making and characterize how moral processes are computed in the brain. Moral dilemma can be modeled as value-based decisions that weigh self-interests against moral costs/harm to others and different types of prediction errors can be distinguished in different aspects of moral learning. These key computational signals help to describe moral choices and moral learning at an algorithmic level and to reveal how these cognitive operations are implemented in the brain. This researches provide a foundation to account for the neurocomputational mechanisms underlying moral decision making.