What does embodiment mean? Is it a running process? Is it required in order to be adaptive? Is it important to distinguish between high-level and low-level cognition processing in order to talk about embodiment and adaptability? Is there a distinction between social embodiment and self-embodiment? What are the best models for behaviour and embodiment? Those questions have been wandering in our minds for a long time, and they have encouraged us to organise a forum to discuss about the meaning and the role of adaptability and embodiment in Multi-Agent Systems (MAS), our subject of research.