Variation in genome structure is an important source of human genetic polymorphism: It affects a large proportion of the genome and has a variety of phenotypic consequences relevant to health and disease. In spite of this, human genome structure variation is incompletely characterized due to a lack of approaches for discovering a broad range of structural variants in a global, comprehensive fashion. We addressed this gap with Optical Mapping, a high-throughput, high-resolution single-molecule system for studying genome structure. We used Optical Mapping to create genome-wide restriction maps of a complete hydatidiform mole and three lymphoblast-derived cell lines, and we validated the approach by demonstrating a strong concordance with existing methods. We also describe thousands of new variants with sizes ranging from kb to Mb.