Insects possess small brains but exhibit sophisticated behavioral performances. Recent works have reported the existence of unsuspected cognitive capabilities in various insect species, which go beyond the traditional studied framework of simple associative learning. In this study, I focus on capabilities such as attention, social learning, individual recognition, concept learning, and metacognition, and discuss their presence and mechanistic bases in insects. I analyze whether these behaviors can be explained on the basis of elemental associative learning or, on the contrary, require higher‐order explanations. In doing this, I highlight experimental challenges and suggest future directions for investigating the neurobiology of higher‐order learning in insects, with the goal of uncovering l architectures underlying cognitive processing. WIREs Cogn Sci 2015, 6:383–395. doi: 10.1002/wcs.1348This article is categorized under: Psychology > Learning Neuroscience > Behavior Neuroscience > Cognition