Group synchronization is a mathematical framework used in a variety of applications, such as computer vision, to situate a set of objects given their pairwise relative positions and orientations subjected to noise. More formally, synchronization estimates a set of group elements given some of their noisy pairwise ratios. In this talk I will present an entirely new view on the task of group synchronization by considering the natural higher-order structures that relate the relative orientations of triples or n-wise sets of objects. Examples of these structures include triples of so-called ‘common lines’ in cryo-EM and trifocal tensors in multi-view geometry. Thus far very little mathematical or computational work has explored synchronizing these higher-order measurements. I will introduce the problem of higher-order group synchronization and discuss the formal foundations of synchronizability in this setting. Then I will present a message passing algorithm to solve the problem and compare its performance to classical pairwise synchronization algorithms.