In this chapter, concepts from physics of complex systems are applied to understand the collective behavior of neuronal cultures, in which an ensemble of initially isolated neurons self-organize and connect to one another to exhibit spontaneous activity with non-trivial dynamics. These cultures are an important experimental model since they allow to study, and even act on, the ensemble of neurons in a controlled manner. Specifically, here we investigate how spatial constraints in the arrangement of neurons and connections on the substrate they grow orchestrate the collective behavior of the emerging network, for instance by shaping the richness of spontaneous activity patterns or the velocity of propagating fronts. We also investigate the importance of the balance between excitatory and inhibitory connections in modulating the repertoire of activity patterns. Given the controllability and versatility of neuronal cultures, we also shed light on the use of numerical models to illustrate their potential in reproducing experimental behavior with relatively simple concepts, reveal the key factors influencing network dynamics, and make predictions. Finally, we discuss the medical applications of neuronal cultures together with their limitations and drawbacks.