This paper examines the interdisciplinary research question of how to integrate Computational Argumentation, as studied in AI, with Cognition, as can be found in Cognitive Science, Linguistics, and Philosophy. It stems from the work of the 1st Workshop on Computational Argumentation and Cognition (COGNITAR), which was organized as part of the 24th European Conference on Artificial Intelligence (ECAI), and took place virtually on September 8th, 2020. The paper begins with a brief presentation of the scientific motivation for the integration of Computational Argumentation and Cognition, arguing that within the context of Human-Centric AI the use of theory and methods from Computational Argumentation for the study of Cognition can be a promising avenue to pursue. A short summary of each of the workshop presentations is given showing the wide spectrum of problems where the synthesis of the theory and methods of Computational Argumentation with other approaches that study Cognition can be applied. The paper presents the main problems and challenges in the area that would need to be addressed, both at the scientific level but also at the epistemological level, particularly in relation to the synthesis of ideas and approaches from the various disciplines involved.