Computing consistent maps (i.e., dense correspondences or rigid transformations) among a collection of objects is a fundamental problem across many applications areas including 3D reconstruction from images and 3D scans. This talk will begin with surveying classical optimization-based techniques. We will then make a connection between map synchronization and generative models. The talk will focus on a series of work on map synchronization by learning shape generative models from both deformable shapes and man-made shapes. We will conclude the talk by discussing future directions.