Just as networks of neurons create structured thoughts beyond the ken of any individual neuron, so people spontaneously organize themselves into groups to create emergent organizations that no individual may intend, comprehend, or even perceive. Recent technological advances have provided us with unprecedented opportunities for conducting controlled, laboratory experiments on human collective behavior. We describe two experimental paradigms where we attempt to build predictive bridges between the beliefs, goals, and cognitive capacities of individuals and group-level patterns, showing how the members of a group dynamically allocate themselves to resources, and how innovations are spread in a social network. Agent-based computational models have provided useful explanatory and predictive accounts. Together, the models and experiments point to tradeoffs between exploration and exploitation, compromises between individuals using their own innovations and innovations obtained from their peers, and the emergence of group-level organizations such as population waves, bandwagon effects, and spontaneous specialization.