In this paper I discuss the relevance of asymmetric processes in living systems, both in a procedural and structural perspective. I do not consider behavior as ahistorical logical problem-solving. Rather I emphasize the anticipation-driven nature of behavior and hence cognition. On a structural level it is evident that the growth of behavioral competence, similar to biological structures, has to build on previously available components. However, reversibility can occur. Finally I will outline the implications of asymmetry for the design of artificial life systems.