Insect societies are the leading examples of collective cognition by social groups. Much like a single animal, a colony of ants can evaluate its surroundings, process information, and make decisions. Cognition emerges from a network of interacting ants, just as individual cognition emerges from interactions among neurons in the brain. The special appeal of these societies is that their parts—individual insects—are themselves complex cognitive entities, providing a unique opportunity to study the interplay between information processing at these two levels. In this talk I will show how individual behavioral rules and communication networks allow many poorly informed ants to make effective collective decisions. I will further show how colonies amplify the limited cognitive capacity of single ants and how they evade certain irrational consequences of individual choice. Finally, I will consider the limits of collective cognition by exploring when it can improve performance by integrating multiple agents, and when it can instead lead to harmful information cascades.