The claustrum is a thin subcortical structure that presents an extensive reciprocal connectivity with the entire neocortex. Despite this broad connectivity, the function of the claustrum remains largely unknown. To probe its function, we used a combination of otptogenetic and chemogenetic tools to manipulate the activity of claustrum glutamatergic projection neurons during various behaviors in mice. We demonstrated that disturbing the activity of the claustrum impairs the ability of mice to perform extradimensional shifts during an attentional set-shifting task, suggesting that the claustrum plays a role in executive functions. We also showed that decreasing the activity of the claustrum during fear conditioning acquisition or consolidation impairs the freezing response of mice in subsequent context recalls, indicating that the claustrum participates to the acquisition and consolidation of contextual memory. The claustrum is therefore a multifunctional structure, being involved in at least two different high-order cognitive processes: executive functions and memory.