“Cognitive enrichment” is a subset of enrichment that has gained interest from researchers over the past decade, particularly those working in zoos. This review explores the forms of cognitive enrichment that have been attempted for laboratory, farmed and zoo animals with a focus on the latter, including various definitions, aims, and approaches. This review reveals the fundamental theoretical and practical problems associated with cognitive enrichment, leading to recommendations for further research in this field. Critically, more research is needed to elucidate what makes challenges appropriate for certain taxa, acknowledging that individual differences exist. Going forward, we should be prepared to incorporate more computer technology into cognitive tasks, and examine novel welfare indicators such as flow, competence, and agency.