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In this tutorial, we first introduce the fundamentals of cycle-consistency and review the broad range of studies that make use of it. Next, we cover different techniques for solving multiview synchronization problems in computer vision, or in other words for achieving cycle consistency. Several techniques including graph theory, combinatorial optimization, Riemannian geometry, spectral decomposition, (non-)convex optimization, and MAP inference will be addressed. Besides optimization techniques, we will also discuss the uncertainty and ambiguities inherent either in the data or in the model and show how the existing tools can be augmented to yield this valuable piece of information. We will finally showcase the applications of synchronizing linear/non-linear maps. Tools and methods presented in this tutorial are beneficial to a large audience as the synchronization is a common technique across several sub-fields of computer vision.