For over a century, researchers have been investigating collective cognition, in which a group of individuals together processes information and acts as a single cognitive unit. However, we still know little about the circumstances under which groups achieve better (or worse) decisions than individuals. To address this question my research applies concepts and methods from psychology to both individuals and groups in order to directly compare their cognitive abilities. As model systems I use house-hunting by the ant Temnothorax rugatulus, and navigation by the homing pigeon, Columba livia. My work has shown that 1) rational group decisions can emerge from interactions among irrational individuals, 2) groups can process more information and thus are less prone to cognitive overload than individuals, and 3) groups show more precise discrimination than individuals, but individuals make better decisions than groups for easy discrimination tasks. Furthermore, my recent research has shown, for the first time in a non-human species, that group decisions are influenced by past experiences and improve progressively, a phenomenon known as cumulative cultural evolution. By combining empirical data and models I elucidate the emergent processes of collective cognition and suggest how and when groups (fail to) achieve higher cognitive performance than individuals.