Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge in both theoretical and empirical realms. The present work shows how integrating approaches from computational algebraic topology and dynamical systems may help us meet this challenge. In particular, we focus on the application of multiscale topological analysis to coordinated rhythmic processes. First, theoretical arguments are introduced as to why certain topological features and their scale-dependency are highly relevant to understanding complex collective dynamics. Second, we propose a method to capture such dynamically relevant topological information using persistent homology, which allows us to effectively construct a multiscale topological portrait of rhythmic coordination. Finally, the method is put to test in detecting transitions in real data from an experiment of rhythmic coordination in ensembles of interacting humans. The recurrence plots of topological portraits highlight collective transitions in coordination patterns that were elusive to more traditional methods. This sensitivity to collective transitions would be lost if the behavioral dynamics of individuals were treated as separate degrees of freedom instead of constituents of the topology that they collectively forge. Such multiscale topological portraits highlight collective aspects of coordination patterns that are irreducible to properties of individual parts. The present work demonstrates how the analysis of multiscale coordination dynamics can benefit from topological methods, thereby paving the way for further systematic quantification of complex, high-dimensional dynamics in living systems.in a way that does justice to all relevant scales. In the present work, we propose a topological approach to analyzing dynamic patterns generated by multiscale coordinative structures. Topological methods have been shown to detect dynamic features of systems exhibiting, e.g., stable, spatiotemporal chaos [15,28,29]. Here we leverage existing computational topology tools, principally, persistent homology to capture the scale-dependency of topological features hidden in complex coordination patterns and detect transitions between them.The quantitative and systematic study of multiscale coordinative structures requires data analytic tools that are tuned to capture dynamic features across scales, that is, without predefining a specific scale of analysis or using a different system of measurement for different scales. The development of such tools is challenging since the measurement not only needs to be multiscale in nature, but also dynamically meaningful: it should capture dynamic patterns of coordination and the transition between coordination patterns in time [24,26]. In the present paper, we propose a multiscale topological approach to this problem. Instead of keeping track of individual state variables, ...