The ASCENS project (http://www.ascens-ist.eu/) researches foundations of and software-engineering methods for ensembles - distributed autonomous systems operating in complex environments which can dynamically adapt to changes in their environment or requirements. We will discuss the notions of adaptation, awareness and emergence which play an important role in the development of ensembles. These terms will be made precise by giving a system model for ensembles on which a mathematical theory of adaptation and awareness can be based. Using this theory we can precisely distinguish different kinds of adaptation, such as adaptation to environment, network or goals, and we can discuss how adaptation, awareness and self-awareness are related.