We use quantum gases of dysprosium atoms, which have one of the largest atomic magnetic moments in nature, to study quantum phase transitions to exotic states of matter and implement quantum simulations. We have recently realized the long-sought “supersolid” state of matter, which combines paradoxically superfluidity and the periodic structure of crystals. We are realizing novel quantum gases of dysprosium molecules, to explore the physics of strongly-correlated dipolar matter and perform quantum simulations of related models.