Complex computing systems begin to overwhelm the capacities of software developers and administrators. Self-organization has been a successful strategy of evolution to handle the increasing complexity of organisms with the emergence of novel structures and behavior. Thus, self-organization and emergence are fundamental concepts of organic computing. But these concepts are often used in a more or less intuitive and fuzzy manner. In the theory of complex systems and nonlinear dynamics, self-organization and emergence can be mathematically defined. Actually, these concepts are independent of biological applications, but universal features of dynamical systems. We get an interdisciplinary framework to understand self-organizing complex systems and to ask for applications in organic computing.