Innovative assessments of cross-curricular competencies such as complex problem solving (CPS) have currently received considerable attention in large-scale educational studies. This study investigated the nature of CPS by applying a state-of-the-art approach to assess CPS in high school. We analyzed whether two processes derived from cognitive psychology, knowledge acquisition and knowledge application, could be measured equally well across grades and how these processes differed between grades. Further, relations between CPS, general mental ability (g), academic achievement, and parental education were explored. Hungarian high school students in Grades 5 to 11 (N = 855) completed MicroDYN, which is a computer-based CPS test, and the Culture Fair Test 20-R as a measure of g. Results based on structural equation models showed that empirical modeling of CPS was in line with theories from cognitive psychology such that the two dimensions identified above were found in all grades, and that there was some development of CPS in school, although the Grade 9 students deviated from the general pattern of development. Finally, path analysis showed that CPS was a relevant predictor of academic achievement over and above g. Overall, results of the current study provide support for an understanding of CPS as a cross-curricular skill that is accessible through computer-based assessment and that yields substantial relations to school performance. Thus, the increasing attention CPS has currently received on an international level seems warranted given its high relevance for educational psychologists.