Cognitive modelling is one of the two key themes spanning across the three Research Programmes of ILLC. In the theme many of ILLC research activities in modelling reasoning, language, music, and social cognition come together. Building on a long experience with logic and computations, we work on mathematical models of reasoning, social cognition, grammar, meaning, music, learning and decision making, at both the symbolic and the subsymbolic level. The collaboration between many disciplines — ranging from neuroscience to linguistics — is necessary to make progress in the understanding of these key higher-order cognitive functions and hence ILLC researches within this theme intensively collaborate with other research institutes, among others, we are actively involved in the Research Priority Area Brain & Cognition and Amsterdam Brain & Mind Project.