The theory of nonlinear complex systems has become a proven problem-solving approach in the natural sciences from cosmic and quantum systems to cellular organisms and the brain. Even in modern engineering science self-organizing systems are developed to manage complex networks and processes. It is now recognized that many of our ecological, social, economic, and political problems are also of a global, complex, and nonlinear nature. Modern evolutionary economics can be modelled in the framework of complex systems and nonlinear dynamics. Historically, evolutionary economics was inspired by Schumpeterian concepts of business cycles and innovation dynamics. What are the laws of sociodynamics? What can we learn from nonlinear dynamics for complexity management in social, economic, financial and political systems? Is self-organization an acceptable strategy to handle the complexity in firms, institutions and organizations? The world-wide crisis of financial markets and economies is a challenge for complexity research. Misleading concepts of linear thinking and mild randomness (e.g. Gaussian distributions of Brownian motion) must be overcome by new approaches of nonlinear mathematics (e.g. non-Gaussian distribution), modelling the wild randomness of turbulence at the stock markets. Systemic crises need systemic answers. Nevertheless, human cognitive capabilities are often overwhelmed by the complexity of nonlinear systems they are forced to manage. Traditional mathematical decision theory assumed perfect rationality of economic agents (homo oeconomicus). Herbert Simon, Nobel Prize laureate of economics and one of the leading pioneers of systems science and cognitive science, introduced the principle of bounded rationality. Therefore, we need new insights into the factual microeconomic behaviour of economic agents by methods of humanities, cognitive and social sciences, which are sometimes called ‘experimental economics’. Social and economic dynamics are interdisciplinary challenges of modern complexity research.