Among ecological economists there is high agreement that sustainability can only be achieved by integrating the economic, societal, and ecological dimension of human development. Sustainability therefore is often described as a triangle system. A deeper knowledge on the interrelations between the three subsystems of economy, society, and nature forms the precondition for the development of political steering possibilities. On the one hand, both the socio-economic and the natural system are complex and dynamic systems, characterized by non-linear feedback relations, dis-continuities, and thresholds. On the other hand, crucial differences in the function mechanisms of these three subsystems can be distinguished. With regard to the discussion on sustainable development, we want to provide an overview on the complexity issue, new methodological approaches dealing with this phenomenon, and empirical results. We analyze the similarities as well as the differences of the three subsystems with regard to several parameters like timescales and system resilience. We discuss whether dependencies of the subsystems should be described as mutual or rather unidirectional. In the last ten years a number of scientific approaches have been introduced, which point out how the complexity problem could be included in decision processes. We give a brief summary of some important approaches which are frequently discussed in the literature. Finally, we discuss the chances for an ecological economic policy to deal with the appropriate level of complexity while acknowledging the limited capacity of political decision makers to control complex processes.