This article is about Complex Problem Solving (CPS), its history in a variety of research domains (e.g., human problem solving, expertise, decision making, and intelligence), a formal definition and a process theory of CPS applicable to the interdisciplinary field. CPS is portrayed as (a) knowledge acquisition and (b) knowledge application concerning the goal-oriented control of systems that contain many highly interrelated elements (i.e., complex systems). The impact of implicit and explicit knowledge as well as systematic strategy selection on the solution process are discussed, emphasizing the importance of (1) information generation (due to the initial intransparency of the situation), (2) information reduction (due to the overcharging complexity of the problem's structure), (3) model building (due to the interconnectedness of the variables), (4) dynamic decision making (due to the eigendynamics of the system), and (5) evaluation (due to many, interfering and/or ill-defined goals).