Studying complex problem solving by means of computer-simulated scenarios has become one of the favorite themes of modern theorists in German-speaking countries who are concerned with the psychology of thinking. Following the pioneering work of Dietrich Doerner (University of Bamberg, FRG) in the mid-70s, many new scenarios have been developed and applied in correlational as well as in experimental studies (for a review see Funke, 1988). Instead of studying problem-solving behavior in restricted situations (like the \"Tower of Hanoi\" or \"Cannibals and Missionaries\"; cf. Greeno, 1974; Jeffries, Polson, & Razran, 1977), the new approach focuses on semantically rich domains that provide a touch of reality that has not inherent in the older research (see also Bhaskar & Simon, 1977). In the computer-administered scenario \"LOHHAUSEN\", for instance, subjects have to take over the regentship of a little town (Doerner, Kreuzig, Reither, & Staeudel, 1983). In other work, subjects take over the roles of a manager of a little shop (Putz-Osterloh, 1981), of an engineer in a developmental country (Reither, 1981), or of a pilot flying to the moon (Thalmaier, 1979). In general, the new approach deals with the exploration and control of complex and dynamic systems by human individuals. This chapter is divided into four main parts. First, I give a working definition of what I mean by \"complex problem solving\" and suggest how complex tasks can be profitably analyzed and compared to each other across domains. Second, I summarize recent research on complex problem solving, analyze the main streams of current research, and discuss the underlying principles and mechanisms uncovered so far. Also, I consider how people learn to solve complex problems and discuss expert-novice differences in complex problem solving. Third, I describe my own approach to studying complex problem solving in which it is conceptualized as a dynamic process of knowledge acquisition and of knowledge application. I briefly describe the so-called DYNAMIS project and the DYNAMIS shell for scenario, and report the results of some studies within this framework. Finally, I give perspectives for future research.