The behavior of insects transcends elementary forms of adaptive responding to environmental changes. We discuss examples of exploration, instrumental and observational learning, expectation, learning in a social context, and planning of future actions. We show that learning about sensory cues allows insects to transfer flexibly their responses to novel stimuli attaining thereby different levels of complexity, from basic generalization to categorization and concept learning consistent with rule extraction. We argue that updating of existing memories requires multiple forms of memory processing. A key element in these processes is working memory, an active form of memory considered to allow evaluation of actions on the basis of expected outcome. We discuss which of these cognitive faculties can be traced to specific neural processes and how they relate to the overall organization of the insect brain.