In the first part of this seminar, we will give an overview of collective periodic behaviors in large systems of interacting components. Loosely speaking, such phenomena consist in nearly-periodic oscillations which characterize the long-time dynamics of some macroscopic quantity of the system, and which cannot be ascribed to any external periodic force applied to the system, nor to any oscillatory behavior of its components, but rather arise from the interaction among these latter. Although they are ubiquitous in real-world systems (they are observed for instance in neural networks, predator-prey dynamics, epidemiology), such behaviors are still poorly understood from a theoretical standpoint. In the second part of the seminar, we will present a toy model of interacting diffusions displaying collective oscillations. This will serve as an example of the mechanisms which may originate collective periodic behaviors and to give an idea of the mathematics involved in the rigorous study of such phenomena.