The paper surveys economic aspects of sustainability and the use of complex ecological systems. In a first step, an economist's view of the concept of sustainability is presented. Then, a simple model of the economic use of a dynamic ecological system is discussed. It is shown how economically optimal trajectories look like, in which circumstances it may be optimal to destroy the ecosystem, and which problems arise if this ecosystem is a common-property resource. Extensions of the model that add complexity and uncertainty are referred to briefly. Finally, some economic concepts to determine the value of ecosystems are presented.