We start this article with a historical review before attempting to systematize different positions. The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986). Linking complex problem solving and general mental ability to career advancement: does a transversal skill reveal incremental predictive validity? Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011; Griffin and Care, 2015), to name only a few. Cognitive processes in well-defined and ill-defined problem solving. One competence that seems to be of central importance is the ability to solve complex problems (Mainzer, 2009). doi: 10.3389/fpsyg.2015.01669 Pub Med Abstract | Cross Ref Full Text | Google Scholar Schraw, G., Dunkle, M., and Bendixen, L. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III III) are defined clearly. Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. doi: 10.1037/0033-295X.84.3.231 Pub Med Abstract | Cross Ref Full Text | Google Scholar Osman, M. Controlling uncertainty: a review of human behavior in complex dynamic environments. Early work (see, e.g., Dörner, 1980) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Construct validity of complex problem solving: a comprehensive view on different facets of intelligence and school grades. doi: 10.1016/j.intell.20 Cross Ref Full Text | Google Scholar Kretzschmar, A., and Süß, H.-M. A study on the training of complex problem solving competence. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. doi: 10.11588/jddm.2015.1.15455 Cross Ref Full Text | Google Scholar Lee, H., and Cho, Y. Factors affecting problem finding depending on degree of structure of problem situation. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. 60) The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers (Blech and Funke, 2010; Funke, 2010; Knauff and Wolf, 2010; Leutner et al., 2012; Selten et al., 2012; Wüstenberg et al., 2012; Greiff et al., 2013b; Fischer and Neubert, 2015; Schoppek and Fischer, 2015), papers about measurement issues (Danner et al., 2011a; Greiff et al., 2012, 2015a; Alison et al., 2013; Gobert et al., 2015; Greiff and Fischer, 2013; Herde et al., 2016; Stadler et al., 2016), papers about applications (Fischer and Neubert, 2015; Ederer et al., 2016; Tremblay et al., 2017), papers about differential effects (Barth and Funke, 2010; Danner et al., 2011b; Beckmann and Goode, 2014; Greiff and Neubert, 2014; Scherer et al., 2015; Meißner et al., 2016; Wüstenberg et al., 2016), one paper about developmental effects (Frischkorn et al., 2014), one paper with a neuroscience background (Osman, 2012), papers about cultural differences (Güss and Dörner, 2011; Sonnleitner et al., 2014; Güss et al., 2015), papers about validity issues (Goode and Beckmann, 2010; Greiff et al., 2013c; Schweizer et al., 2013; Mainert et al., 2015; Funke et al., 2017; Greiff et al., 2017, 2015b; Kretzschmar et al., 2016; Kretzschmar, 2017), review papers and meta-analyses (Osman, 2010; Stadler et al., 2015), and finally books (Qudrat-Ullah, 2015; Csapó and Funke, 2017b) and book chapters (Funke, 2012; Hotaling et al., 2015; Funke and Greiff, 2017; Greiff and Funke, 2017; Csapó and Funke, 2017a; Fischer et al., 2017; Molnàr et al., 2017; Tobinski and Fritz, 2017; Viehrig et al., 2017). Predicting complex problem solving and school grades with working memory and ability self-concept.