The MUHAI project introduces meaning and understanding in artificial intelligence. The project tackles the foundational question of meaning by developing computational models of narrative construction. MUHAI uses common sense pragmatic knowledge about the world needed for the domain of cooking and social knowledge needed for coming up with, understanding and checking data stories about inequality in society. The project relies on many existing techniques of AI ranging from deep learning networks to knowledge graphs, but will push their boundaries and develop new techniques all operating in the service of giving AI systems a better grip on meaning and thus on explanation and other key issues for achieving human-centric AI. The final outcome of MUHAI is to push the state of the art in cognitive home robotics, particularly for food production and the management of food resources, and to provide tools for social scientists to better understand social phenomena, as for example the persistence of inequality in our society.