This chapter presents research on moral judgment from the beginning of the 20th century to the present day. First, the authors will present the contribution of Piaget and Kohlberg's work on moral development from childhood to adulthood as well as the work of Gilligan on moral orientation and the difference observed between men and women. Then, the authors will analyze underlying structures of moral judgment in the light of the Dual Process Theory with two systems: system 1: quick, deontological, emotional, intuitive, automatic, and system 2: slow, utilitarian, rational, controlled, involved in human reasoning. Finally, the model of Dual Process Theory will be confronted with data from moral judgment experiments, run on elderly adults with Alzheimer's disease, teenagers with Autism Spectrum Disorder, and children and teenagers with intellectual disability in order to understand how cognitive impairment affects the structures and components of moral judgment.