From flocking birds, to organ generation, to swarming bacterial colonies, biological systems often exhibit collective behaviors. Here, we review recent advances in our understanding of collective dynamics in cell populations. We argue that understanding population-level oscillations requires examining the system under consideration at three different levels of complexity: at the level of isolated cells, homogenous populations, and spatially structured populations. We discuss the experimental and theoretical challenges this poses and highlight how new experimental techniques, when combined with conceptual tools adapted from physics, may help us overcome these challenges.